Kortit II

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<int> vi;

#define F first
#define S second
#define PB push_back
#define MP make_pair
#define FOR(i,a,b) for (ll i = a; i < b; i++)

ll mod=1e9+7;
vector<vector<ll>> bin = {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 7, 21, 35, 35, 21, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770, 497420, 646646, 705432, 646646, 497420, 319770, 170544, 74613, 26334, 7315, 1540, 231, 22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 23, 253, 1771, 8855, 33649, 100947, 245157, 490314, 817190, 1144066, 1352078, 1352078, 1144066, 817190, 490314, 245157, 100947, 33649, 8855, 1771, 253, 23, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 25, 300, 2300, 12650, 53130, 177100, 480700, 1081575, 2042975, 3268760, 4457400, 5200300, 5200300, 4457400, 3268760, 2042975, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, 5311735, 7726160, 9657700, 10400600, 9657700, 7726160, 5311735, 3124550, 1562275, 657800, 230230, 65780, 14950, 2600, 325, 26, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 27, 351, 2925, 17550, 80730, 296010, 888030, 2220075, 4686825, 8436285, 13037895, 17383860, 20058300, 20058300, 17383860, 13037895, 8436285, 4686825, 2220075, 888030, 296010, 80730, 17550, 2925, 351, 27, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 28, 378, 3276, 20475, 98280, 376740, 1184040, 3108105, 6906900, 13123110, 21474180, 30421755, 37442160, 40116600, 37442160, 30421755, 21474180, 13123110, 6906900, 3108105, 1184040, 376740, 98280, 20475, 3276, 378, 28, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 29, 406, 3654, 23751, 118755, 475020, 1560780, 4292145, 10015005, 20030010, 34597290, 51895935, 67863915, 77558760, 77558760, 67863915, 51895935, 34597290, 20030010, 10015005, 4292145, 1560780, 475020, 118755, 23751, 3654, 406, 29, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 30, 435, 4060, 27405, 142506, 593775, 2035800, 5852925, 14307150, 30045015, 54627300, 86493225, 119759850, 145422675, 155117520, 145422675, 119759850, 86493225, 54627300, 30045015, 14307150, 5852925, 2035800, 593775, 142506, 27405, 4060, 435, 30, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315, 44352165, 20160075, 7888725, 2629575, 736281, 169911, 31465, 4495, 465, 31, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 32, 496, 4960, 35960, 201376, 906192, 3365856, 10518300, 28048800, 64512240, 129024480, 225792840, 347373600, 471435600, 565722720, 601080390, 565722720, 471435600, 347373600, 225792840, 129024480, 64512240, 28048800, 10518300, 3365856, 906192, 201376, 35960, 4960, 496, 32, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 33, 528, 5456, 40920, 237336, 1107568, 4272048, 13884156, 38567100, 92561040, 193536720, 354817320, 573166440, 818809200, 37158313, 166803103, 166803103, 37158313, 818809200, 573166440, 354817320, 193536720, 92561040, 38567100, 13884156, 4272048, 1107568, 237336, 40920, 5456, 528, 33, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 34, 561, 5984, 46376, 278256, 1344904, 5379616, 18156204, 52451256, 131128140, 286097760, 548354040, 927983760, 391975633, 855967513, 203961416, 333606206, 203961416, 855967513, 391975633, 927983760, 548354040, 286097760, 131128140, 52451256, 18156204, 5379616, 1344904, 278256, 46376, 5984, 561, 34, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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                        {1, 36, 630, 7140, 58905, 376992, 1947792, 8347680, 30260340, 94143280, 254186856, 600805296, 251677693, 310789586, 796297179, 567902525, 307872061, 597496544, 75135237, 597496544, 307872061, 567902525, 796297179, 310789586, 251677693, 600805296, 254186856, 94143280, 30260340, 8347680, 1947792, 376992, 58905, 7140, 630, 36, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 37, 666, 7770, 66045, 435897, 2324784, 10295472, 38608020, 124403620, 348330136, 854992152, 852482989, 562467279, 107086758, 364199697, 875774586, 905368605, 672631781, 672631781, 905368605, 875774586, 364199697, 107086758, 562467279, 852482989, 854992152, 348330136, 124403620, 38608020, 10295472, 2324784, 435897, 66045, 7770, 666, 37, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 38, 703, 8436, 73815, 501942, 2760681, 12620256, 48903492, 163011640, 472733756, 203322281, 707475134, 414950261, 669554037, 471286455, 239974276, 781143184, 578000379, 345263555, 578000379, 781143184, 239974276, 471286455, 669554037, 414950261, 707475134, 203322281, 472733756, 163011640, 48903492, 12620256, 2760681, 501942, 73815, 8436, 703, 38, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 39, 741, 9139, 82251, 575757, 3262623, 15380937, 61523748, 211915132, 635745396, 676056037, 910797415, 122425388, 84504291, 140840485, 711260731, 21117453, 359143556, 923263934, 923263934, 359143556, 21117453, 711260731, 140840485, 84504291, 122425388, 910797415, 676056037, 635745396, 211915132, 61523748, 15380937, 3262623, 575757, 82251, 9139, 741, 39, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 40, 780, 9880, 91390, 658008, 3838380, 18643560, 76904685, 273438880, 847660528, 311801426, 586853445, 33222796, 206929679, 225344776, 852101216, 732378184, 380261009, 282407483, 846527861, 282407483, 380261009, 732378184, 852101216, 225344776, 206929679, 33222796, 586853445, 311801426, 847660528, 273438880, 76904685, 18643560, 3838380, 658008, 91390, 9880, 780, 40, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 41, 820, 10660, 101270, 749398, 4496388, 22481940, 95548245, 350343565, 121099401, 159461947, 898654871, 620076241, 240152475, 432274455, 77445985, 584479393, 112639186, 662668492, 128935337, 128935337, 662668492, 112639186, 584479393, 77445985, 432274455, 240152475, 620076241, 898654871, 159461947, 121099401, 350343565, 95548245, 22481940, 4496388, 749398, 101270, 10660, 820, 41, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 42, 861, 11480, 111930, 850668, 5245786, 26978328, 118030185, 445891810, 471442966, 280561348, 58116811, 518731105, 860228716, 672426930, 509720440, 661925378, 697118579, 775307678, 791603829, 257870674, 791603829, 775307678, 697118579, 661925378, 509720440, 672426930, 860228716, 518731105, 58116811, 280561348, 471442966, 445891810, 118030185, 26978328, 5245786, 850668, 111930, 11480, 861, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 43, 903, 12341, 123410, 962598, 6096454, 32224114, 145008513, 563921995, 917334776, 752004314, 338678159, 576847916, 378959814, 532655639, 182147363, 171645811, 359043950, 472426250, 566911500, 49474496, 49474496, 566911500, 472426250, 359043950, 171645811, 182147363, 532655639, 378959814, 576847916, 338678159, 752004314, 917334776, 563921995, 145008513, 32224114, 6096454, 962598, 123410, 12341, 903, 43, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 44, 946, 13244, 135751, 1086008, 7059052, 38320568, 177232627, 708930508, 481256764, 669339083, 90682466, 915526075, 955807730, 911615453, 714803002, 353793174, 530689761, 831470200, 39337743, 616385996, 98948992, 616385996, 39337743, 831470200, 530689761, 353793174, 714803002, 911615453, 955807730, 915526075, 90682466, 669339083, 481256764, 708930508, 177232627, 38320568, 7059052, 1086008, 135751, 13244, 946, 44, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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                        {1, 46, 1035, 15180, 163185, 1370754, 9366819, 53524680, 260932815, 101716323, 76350393, 340783105, 910617389, 766230083, 877542332, 738756967, 493841617, 695014617, 953079104, 246642882, 232967890, 526531675, 371058720, 430669969, 371058720, 526531675, 232967890, 246642882, 953079104, 695014617, 493841617, 738756967, 877542332, 766230083, 910617389, 340783105, 76350393, 101716323, 260932815, 53524680, 9366819, 1370754, 163185, 15180, 1035, 46, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 47, 1081, 16215, 178365, 1533939, 10737573, 62891499, 314457495, 362649138, 178066716, 417133498, 251400487, 676847465, 643772408, 616299292, 232598577, 188856227, 648093714, 199721979, 479610772, 759499565, 897590395, 801728689, 801728689, 897590395, 759499565, 479610772, 199721979, 648093714, 188856227, 232598577, 616299292, 643772408, 676847465, 251400487, 417133498, 178066716, 362649138, 314457495, 62891499, 10737573, 1533939, 178365, 16215, 1081, 47, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 48, 1128, 17296, 194580, 1712304, 12271512, 73629072, 377348994, 677106633, 540715854, 595200214, 668533985, 928247952, 320619866, 260071693, 848897869, 421454804, 836949941, 847815693, 679332751, 239110330, 657089953, 699319077, 603457371, 699319077, 657089953, 239110330, 679332751, 847815693, 836949941, 421454804, 848897869, 260071693, 320619866, 928247952, 668533985, 595200214, 540715854, 677106633, 377348994, 73629072, 12271512, 1712304, 194580, 17296, 1128, 48, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066, 54455620, 217822480, 135916061, 263734192, 596781930, 248867811, 580691559, 108969555, 270352666, 258404738, 684765627, 527148437, 918443081, 896200283, 356409023, 302776441, 302776441, 356409023, 896200283, 918443081, 527148437, 684765627, 258404738, 270352666, 108969555, 580691559, 248867811, 596781930, 263734192, 135916061, 217822480, 54455620, 450978066, 85900584, 13983816, 1906884, 211876, 18424, 1176, 49, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 50, 1225, 19600, 230300, 2118760, 15890700, 99884400, 536878650, 505433686, 272278100, 353738541, 399650253, 860516122, 845649741, 829559370, 689661114, 379322221, 528757404, 943170365, 211914057, 445591511, 814643357, 252609299, 659185464, 605552882, 659185464, 252609299, 814643357, 445591511, 211914057, 943170365, 528757404, 379322221, 689661114, 829559370, 845649741, 860516122, 399650253, 353738541, 272278100, 505433686, 536878650, 99884400, 15890700, 2118760, 230300, 19600, 1225, 50, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 51, 1275, 20825, 249900, 2349060, 18009460, 115775100, 636763050, 42312329, 777711786, 626016641, 753388794, 260166368, 706165856, 675209104, 519220477, 68983328, 908079625, 471927762, 155084415, 657505568, 260234861, 67252649, 911794763, 264738339, 264738339, 911794763, 67252649, 260234861, 657505568, 155084415, 471927762, 908079625, 68983328, 519220477, 675209104, 706165856, 260166368, 753388794, 626016641, 777711786, 42312329, 636763050, 115775100, 18009460, 2349060, 249900, 20825, 1275, 51, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 52, 1326, 22100, 270725, 2598960, 20358520, 133784560, 752538150, 679075379, 820024115, 403728420, 379405428, 13555155, 966332224, 381374953, 194429574, 588203805, 977062953, 380007380, 627012177, 812589983, 917740429, 327487510, 979047412, 176533095, 529476678, 176533095, 979047412, 327487510, 917740429, 812589983, 627012177, 380007380, 977062953, 588203805, 194429574, 381374953, 966332224, 13555155, 379405428, 403728420, 820024115, 679075379, 752538150, 133784560, 20358520, 2598960, 270725, 22100, 1326, 52, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                        {1, 53, 1378, 23426, 292825, 2869685, 22957480, 154143080, 886322710, 431613522, 499099487, 223752528, 783133848, 392960583, 979887379, 347707170, 575804527, 782633379, 565266751, 357070326, 7019550, 439602153, 730330405, 245227932, 306534915, 155580500, 706009773, 706009773, 155580500, 306534915, 245227932, 730330405, 439602153, 7019550, 357070326, 565266751, 782633379, 575804527, 347707170, 979887379, 392960583, 783133848, 223752528, 499099487, 431613522, 886322710, 154143080, 22957480, 2869685, 292825, 23426, 1378, 53, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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                        {1, 94, 4371, 134044, 3049501, 54891018, 814216767, 235867858, 315062940, 677268077, 256778616, 324491238, 744397719, 695431738, 309283601, 316179196, 811134775, 368736003, 77370669, 309482676, 160560028, 375306764, 154426982, 526901857, 517084653, 247837020, 273105935, 835970504, 714643697, 833327029, 972208557, 845849916, 790267016, 151410748, 918707523, 860641463, 438273502, 254590892, 381886338, 625272691, 984749951, 516499930, 842249913, 716209195, 216515199, 573905779, 546117025, 791779091, 546117025, 573905779, 216515199, 716209195, 842249913, 516499930, 984749951, 625272691, 381886338, 254590892, 438273502, 860641463, 918707523, 151410748, 790267016, 845849916, 972208557, 833327029, 714643697, 835970504, 273105935, 247837020, 517084653, 526901857, 154426982, 375306764, 160560028, 309482676, 77370669, 368736003, 811134775, 316179196, 309283601, 695431738, 744397719, 324491238, 256778616, 677268077, 315062940, 235867858, 814216767, 54891018, 3049501, 134044, 4371, 94, 1, 0, 0, 0, 0, 0, 0},
                        {1, 95, 4465, 138415, 3183545, 57940519, 869107785, 50084618, 550930798, 992331017, 934046693, 581269854, 68888950, 439829450, 4715332, 625462797, 127313964, 179870771, 446106672, 386853345, 470042704, 535866792, 529733746, 681328839, 43986503, 764921673, 520942955, 109076432, 550614194, 547970719, 805535579, 818058466, 636116925, 941677764, 70118264, 779348979, 298914958, 692864394, 636477230, 7159022, 610022635, 501249874, 358749836, 558459101, 932724394, 790420978, 120022797, 337896109, 337896109, 120022797, 790420978, 932724394, 558459101, 358749836, 501249874, 610022635, 7159022, 636477230, 692864394, 298914958, 779348979, 70118264, 941677764, 636116925, 818058466, 805535579, 547970719, 550614194, 109076432, 520942955, 764921673, 43986503, 681328839, 529733746, 535866792, 470042704, 386853345, 446106672, 179870771, 127313964, 625462797, 4715332, 439829450, 68888950, 581269854, 934046693, 992331017, 550930798, 50084618, 869107785, 57940519, 3183545, 138415, 4465, 95, 1, 0, 0, 0, 0, 0},
                        {1, 96, 4560, 142880, 3321960, 61124064, 927048304, 919192403, 601015416, 543261808, 926377703, 515316540, 650158804, 508718400, 444544782, 630178129, 752776761, 307184735, 625977443, 832960017, 856896049, 5909489, 65600531, 211062578, 725315342, 808908176, 285864621, 630019387, 659690626, 98584906, 353506291, 623594038, 454175384, 577794682, 11796021, 849467243, 78263930, 991779352, 329341617, 643636252, 617181657, 111272502, 859999710, 917208937, 491183488, 723145365, 910443775, 457918906, 675792218, 457918906, 910443775, 723145365, 491183488, 917208937, 859999710, 111272502, 617181657, 643636252, 329341617, 991779352, 78263930, 849467243, 11796021, 577794682, 454175384, 623594038, 353506291, 98584906, 659690626, 630019387, 285864621, 808908176, 725315342, 211062578, 65600531, 5909489, 856896049, 832960017, 625977443, 307184735, 752776761, 630178129, 444544782, 508718400, 650158804, 515316540, 926377703, 543261808, 601015416, 919192403, 927048304, 61124064, 3321960, 142880, 4560, 96, 1, 0, 0, 0, 0},
                        {1, 97, 4656, 147440, 3464840, 64446024, 988172368, 846240700, 520207812, 144277217, 469639504, 441694236, 165475337, 158877197, 953263182, 74722904, 382954883, 59961489, 933162178, 458937453, 689856059, 862805538, 71510020, 276663109, 936377920, 534223511, 94772790, 915884008, 289710006, 758275532, 452091197, 977100329, 77769415, 31970059, 589590703, 861263264, 927731173, 70043275, 321120962, 972977869, 260817902, 728454159, 971272212, 777208640, 408392418, 214328846, 633589133, 368362674, 133711117, 133711117, 368362674, 633589133, 214328846, 408392418, 777208640, 971272212, 728454159, 260817902, 972977869, 321120962, 70043275, 927731173, 861263264, 589590703, 31970059, 77769415, 977100329, 452091197, 758275532, 289710006, 915884008, 94772790, 534223511, 936377920, 276663109, 71510020, 862805538, 689856059, 458937453, 933162178, 59961489, 382954883, 74722904, 953263182, 158877197, 165475337, 441694236, 469639504, 144277217, 520207812, 846240700, 988172368, 64446024, 3464840, 147440, 4656, 97, 1, 0, 0, 0},
                        {1, 98, 4753, 152096, 3612280, 67910864, 52618385, 834413061, 366448505, 664485029, 613916721, 911333740, 607169573, 324352534, 112140372, 27986079, 457677787, 442916372, 993123667, 392099624, 148793505, 552661590, 934315558, 348173129, 213041022, 470601424, 628996301, 10656791, 205594007, 47985531, 210366722, 429191519, 54869737, 109739474, 621560762, 450853960, 788994430, 997774448, 391164237, 294098824, 233795764, 989272061, 699726364, 748480845, 185601051, 622721264, 847917979, 1951800, 502073791, 267422234, 502073791, 1951800, 847917979, 622721264, 185601051, 748480845, 699726364, 989272061, 233795764, 294098824, 391164237, 997774448, 788994430, 450853960, 621560762, 109739474, 54869737, 429191519, 210366722, 47985531, 205594007, 10656791, 628996301, 470601424, 213041022, 348173129, 934315558, 552661590, 148793505, 392099624, 993123667, 442916372, 457677787, 27986079, 112140372, 324352534, 607169573, 911333740, 613916721, 664485029, 366448505, 834413061, 52618385, 67910864, 3612280, 152096, 4753, 98, 1, 0, 0},
                        {1, 99, 4851, 156849, 3764376, 71523144, 120529249, 887031446, 200861559, 30933527, 278401743, 525250454, 518503306, 931522107, 436492906, 140126451, 485663866, 900594159, 436040032, 385223284, 540893129, 701455095, 486977141, 282488680, 561214151, 683642446, 99597718, 639653092, 216250798, 253579538, 258352253, 639558241, 484061256, 164609211, 731300236, 72414715, 239848383, 786768871, 388938678, 685263061, 527894588, 223067818, 688998418, 448207202, 934081896, 808322315, 470639236, 849869779, 504025591, 769496025, 769496025, 504025591, 849869779, 470639236, 808322315, 934081896, 448207202, 688998418, 223067818, 527894588, 685263061, 388938678, 786768871, 239848383, 72414715, 731300236, 164609211, 484061256, 639558241, 258352253, 253579538, 216250798, 639653092, 99597718, 683642446, 561214151, 282488680, 486977141, 701455095, 540893129, 385223284, 436040032, 900594159, 485663866, 140126451, 436492906, 931522107, 518503306, 525250454, 278401743, 30933527, 200861559, 887031446, 120529249, 71523144, 3764376, 156849, 4851, 99, 1, 0},
                        {1, 100, 4950, 161700, 3921225, 75287520, 192052393, 7560688, 87892998, 231795086, 309335270, 803652197, 43753753, 450025406, 368015006, 576619357, 625790317, 386258018, 336634184, 821263316, 926116413, 242348217, 188432229, 769465821, 843702831, 244856590, 783240164, 739250810, 855903890, 469830336, 511931791, 897910494, 123619490, 648670467, 895909447, 803714951, 312263098, 26617247, 175707542, 74201732, 213157642, 750962406, 912066236, 137205613, 382289091, 742404204, 278961544, 320509008, 353895363, 273521609, 538992043, 273521609, 353895363, 320509008, 278961544, 742404204, 382289091, 137205613, 912066236, 750962406, 213157642, 74201732, 175707542, 26617247, 312263098, 803714951, 895909447, 648670467, 123619490, 897910494, 511931791, 469830336, 855903890, 739250810, 783240164, 244856590, 843702831, 769465821, 188432229, 242348217, 926116413, 821263316, 336634184, 386258018, 625790317, 576619357, 368015006, 450025406, 43753753, 803652197, 309335270, 231795086, 87892998, 7560688, 192052393, 75287520, 3921225, 161700, 4950, 100, 1}};

ll fac(ll n) {

    ll f=1;
    FOR(i,1,n+1) {
        f = (f%mod*i%mod)%mod;
    }
    return f;
}

vector<vector<ll>> im(ll n, ll r) {
    return vector<vector<ll>>(n + 1, vector<ll>(r + 1, -1));
}

ll h(ll n, ll r, vector<vector<ll>> &m) {
    if (n == 0 && r == 0) {
        return 1;
    }
    if (n < 0 || r < 0) {
        return 0;
    }
    if (r > n) {
        return 0;
    }

    if (m[n][r] != -1) {
        return m[n][r];
    }

    m[n][r] = (r%mod * h(n - 1, r, m)%mod + (n - r)%mod * h(n - 1, r - 1, m)%mod + (n - 1)%mod * h(n - 2, r - 1, m)%mod)%mod;

    return m[n][r]%mod;
}

void f() {
    ll n, a, b, t, tm, jm, vm, r;
    cin >> n >> a >> b;
    t = n-a-b;
    if (t<0) {
        cout << 0 << "\n";
        return;
    }
    tm = bin[n][t];
    jm = fac(n);
    vector<vector<ll>> m = im(n-t, a);
    vm = h(n-t, a, m);
    r=((tm%mod*jm%mod)%mod*vm%mod)%(mod);
    cout << r << "\n";
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t;
    cin >> t;
    FOR(i,0,t) {
        f();
    }
}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 2

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 3

Group: 3, 4, 5

Verdict: ACCEPTED

Test 4

Group: 4, 5

Verdict: ACCEPTED

Test 5

Group: 5

Verdict: RUNTIME ERROR

Test 6

Group: 5

Verdict: RUNTIME ERROR