Kortit II

input/code.cpp:13:19: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   13 | void print(vector<auto> v) {
      |                   ^~~~

#include <bits/stdc++.h>

#define F0R(n) for (int i=0; i<n; i++)
#define FOR(i, from, to) for (i = from; i < to; i++)
#define R0F(n) for (int i = n; i>=0; --i)
#define ROF(from, to) for (int i = from; i >= to; --i)

#define ll long long
#define mod (ll) (1e9 + 7)
#define vll vector<ll>
using namespace std;

void print(vector<auto> v) {
	for (auto it = v.begin(); it != v.end(); ++it)
		cout << *it << " ";
	cout << "\n";
}

ll N = 2001;

vll fact_mod(2*N+2, 0);
void build_fact() {
    fact_mod[0] = 1ll;
    ll i;
    FOR (i, 1ll, 2*N+2)
        // fact_mod[i] = fact_mod[i-1]*i;
        (fact_mod[i] = fact_mod[i-1]*i) %= mod;
    // print(fact_mod);
}

vector<vll> nCr_mod(N+1, vll(N+1,0));
void build_nCr() {
    ll n, k;
    nCr_mod[0][0] = 1ll;
    FOR (n, 1, N+1) {
        FOR (k, 0, n+1) {
            if (k == 0)
                nCr_mod[n][k] = 1ll;
            else {
                nCr_mod[n][k] = nCr_mod[n-1][k-1]%mod;
                nCr_mod[n][k] += nCr_mod[n-1][k] % mod;
                nCr_mod[n][k] %= mod;
            }
        }
    }
    /*for (auto v : nCr_mod)
        print(v);*/
}

/*ll nCr(ll n, ll k) {
    if (k <= 0) return 1ll;
    ll ans = 1ll, i;
    FOR (i, n-k+1, n+1)
        ans *= i;
    FOR (i, 1, k+1)
        ans /= i;

    ans %= mod;
    return ans;
}*/

vector<vll> dp(N, vll(N, 0));
void build() {
    dp[0][0] = 1ll;
    ll a, b;
    FOR (a, 1, N) {
        FOR (b, 1, N) {
            (dp[a][b] = dp[a][b-1]*a) %= mod;
            (dp[a][b] += dp[a-1][b]*b) %= mod;
            (dp[a][b] += dp[a-1][b-1]*(a+b-1ll)) %= mod;
            // (dp[a][b] *= fact_mod[a+b]) %= mod;
        }
    }
}

void soln() {
    ll n, a, b, ans;
    cin >> n >> a >> b;
    if (a+b>n) {
        ans = 0;
        cout << ans << "\n";
        return;
    }

    ans = dp[a][b];
    // cout << ans << "\n";
    ans *= nCr_mod[n][a+b];
    ans %= mod;
    // cout << ans << "\n";
    ans *= fact_mod[n];
    ans %= mod;
    cout << ans << "\n";
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    build_fact();
    build_nCr();
    build();

    int tc;
    cin >> tc;
    while (tc--) soln();
    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