Kortit II

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

const int MOD = 1000000007;

vector<vector<int>> Eulerian;
vector<ll> factorial, inv_factorial;
vector<vector<ll>> binomial;

void calc_eulerian(int max_n) {
    Eulerian.assign(max_n + 1, vector<int>(max_n + 1, 0));
    Eulerian[0][0] = 1;
    for (int i = 1; i <= max_n; i++) {
        for (int j = 0; j <= i - 1; j++) {
            if (j == 0) {
                Eulerian[i][j] = 1;
            } else {
                Eulerian[i][j] = ((ll)(i - j) * Eulerian[i - 1][j - 1] % MOD +
                                  (ll)(j + 1) * Eulerian[i - 1][j] % MOD) % MOD;
            }
        }
    }
}

ll power_mod(ll a, ll b, ll mod_val) {
    ll res = 1;
    a %= mod_val;
    while (b > 0) {
        if (b & 1LL) {
            res = res * a % mod_val;
        }
        a = a * a % mod_val;
        b >>= 1LL;
    }
    return res;
}

void calc_factorials(int n_max) {
    factorial.assign(n_max + 1, 1LL);
    inv_factorial.assign(n_max + 1, 1LL);
    for (int i = 1; i <= n_max; ++i) {
        factorial[i] = factorial[i - 1] * i % MOD;
    }
    inv_factorial[n_max] = power_mod(factorial[n_max], MOD - 2, MOD);
    for (int i = n_max - 1; i >= 0; i--) {
        inv_factorial[i] = inv_factorial[i + 1] * (i + 1) % MOD;
    }
}

void calc_binomial(int max_n) {
    binomial.assign(max_n + 1, vector<ll>(max_n + 1, 0));
    for (int i = 0; i <= max_n; ++i) {
        binomial[i][0] = 1;
        for (int j = 1; j <= i; ++j) {
            binomial[i][j] = (binomial[i - 1][j - 1] + binomial[i - 1][j]) % MOD;
        }
    }
}

ll D_E(int m, int b) {
    ll total = 0;
    if (Eulerian[m][b] == 0) return total;

    ll sign = 1;
    for (int k = 0; k <= m; k++) {
        if (b > m - k || m - k < 0) continue;

        ll Cmk = binomial[m][k];        
        ll Ak = Eulerian[m - k][b];
        total = (total + sign * (Cmk * Ak % MOD)) % MOD;
        sign = MOD - sign;
    }
    return total;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int T;
    cin >> T;

    vector<tuple<int, int, int>> tests(T);
    int max_n = 0;
    for (auto &x : tests) {
        cin >> get<0>(x) >> get<1>(x) >> get<2>(x);
        max_n = max(max_n, get<0>(x));
    }

    calc_factorials(max_n);
    calc_eulerian(max_n);
    calc_binomial(max_n);

    for (auto &x : tests) {
        int n, a, b;
        tie(n, a, b) = x;
        int c = n - a - b;
        if (c < 0 || c > n || a < 0 || b < 0) {
            cout << "0\n";
            continue;
        }

        ll C_nc = binomial[n][c];

        ll f = (n - c >= 0 && b <= (n - c)) ? D_E(n - c, b) : 0LL;
        
        ll total = factorial[n] * C_nc % MOD;
        total = total * f % MOD;
        cout << total << "\n";
    }

    return 0;
}

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: ACCEPTED

Test 6

Group: 5

Verdict: ACCEPTED