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>> mb;
vector<vector<ll>> m;

ll fac(ll n) {

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

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

int bin(ll n, ll k, vector<vector<ll>> &m)
{
    if (k > n)
        return 0;
    if (k == 0 || k == n)
        return 1;

    if (m[n][k] != -1) {
        return m[n][k];
    }
    m[n][k] = bin(n - 1, k - 1, m)%mod + bin(n - 1, k, m)%mod;
    return m[n][k]%mod;
}

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, mb);
    jm = fac(n);
    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);
    mb = bim(2000, 2000);
    m = im(2000, 2000);
    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: ACCEPTED

Test 6

Group: 5

Verdict: ACCEPTED