Kortit II

// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

#include <algorithm>
#include <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<class T> using indexed_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

using ll = long long;
using ull = unsigned long long;
using ld = long double;

using pii = pair<int, int>;
using pll = pair<ll, ll>;

// const ll M = 998244353;
const ll M = 1e9 + 7;
// ll M;


#define all(v) (v).begin(), (v).end()
#define ff first
#define ss second
#define PI 3.141592653589793238462643383279502884L

const ll INFL = 1e18;
const int INF = 1e9;
const ll maxN = 5e5+1;

ll inv(ll a) {
    return a<=1 ? a: M - (ll)(M/a) * inv(M%a) % M;
}

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

ll fact[maxN];
ll inv_fact[maxN];
ll t[100][100];

void calc_fact() {
    fact[0] = 1;
    for (int i=1; i<maxN; i++) {
        fact[i] = fact[i-1]*i % M;
        inv_fact[i] = inv(fact[i]);
    }
}

ll nCr(int n, int k) {
    return fact[n] * inv(fact[k]*fact[n-k] % M) % M;
}

void solve() {
    int n, a, b;
    cin >> n >> a >> b;
    if (a+b>n) {
        cout << "0\n";
        return;
    }
    if ((a && !b) || (b && !a)) {
        cout << "0\n";
        return;
    }
    ll ans = fact[n]*nCr(n, n-a-b)%M;
    ans = ans * t[a+b][a] % M;
    cout << ans << '\n';
    
}
int main() {
    calc_fact();
    ios_base::sync_with_stdio(0); cin.tie(NULL);
    cout << setprecision(12);
    for (int sz=1; sz<=8; sz++) {
        for (int i=1; i<=sz; i++) {
            vector<int> p(sz);
            iota(all(p), 0);
            int cur = 0;
            do { 
                int a = 0;
                for (int j=0; j<sz; j++) {
                    if (p[j]==j) {
                        a = -INF;
                        break;
                    }
                    a += p[j]>j;
                }
                cur += a==i;

            } while (next_permutation(all(p)));
            t[sz][i] = cur;
            // cout << cur << ' ';
        }
        // cout << '\n';

    }


    int tc = 1;
    cin >>tc;
    while (tc--) solve();

}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: WRONG ANSWER

Test 2

Group: 2, 3, 4, 5

Verdict: WRONG ANSWER

Test 3

Group: 3, 4, 5

Verdict: WRONG ANSWER

Test 4

Group: 4, 5

Verdict: WRONG ANSWER

Test 5

Group: 5

Verdict: WRONG ANSWER

Test 6

Group: 5

Verdict: WRONG ANSWER