Kortit II

#include <iostream>

using namespace std;

long long FACT[2001] = {};
long long A[2001][2001] = {};
long long C[2001][2001] = {};

const long long MOD = 1000000007;

long long factorial(long long n) {
    if (FACT[n] != 0) return FACT[n];
    if (n == 0) return FACT[n] = 1;
    return FACT[n] = (n * factorial(n - 1)) % MOD;
}

long long a_function(long long n, long long x) {
    if (A[n][x] != 0) return A[n][x];
    if (n == x) return A[n][x] = 0;
    if (x == 0) return A[n][x] = 1;
    return A[n][x] = ((x + 1) * a_function(n - 1, x) % MOD + (n - x) * a_function(n - 1, x - 1) % MOD) % MOD;
}

long long binomal(long long n, long long k) {
    if (C[n][k] != 0) return C[n][k];
    if (k == 0 || k == n) return C[n][k] = 1;
    return C[n][k] = (binomal(n - 1, k) + binomal(n - 1, k - 1)) % MOD;
}

long long d_function(long long n, long long x) {
    long long result = 0;
    for (int i = n; i >= x; i--) {
        long long a = a_function(i, x);
        long long b = binomal(n, n - i);
        result = (result + ((n - i) % 2 == 0 ? (a * b) % MOD : (-(a * b) % MOD + MOD))) % MOD;
    }
    return result;
}

int main() {
    int t;
    cin >> t;

    long long ans[t];

    int n, a, b;

    for (int i = 0; i < t; i++) {
        cin >> n >> a >> b;
        if ((a + b > n) || (a == 0 && b != 0) || (b == 0 && a != 0)) {
            ans[i] = 0;
            continue;
        }
        if (a == 0 || b == 0) {
            ans[i] = factorial(n);
            continue;
        }
        ans[i] = (((d_function(a + b, a) * binomal(n, n - a - b)) % MOD) * factorial(n)) % MOD;
    }

    for (int i = 0; i < t; i++) {
        cout << ans[i] << endl;
    }

    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