Kortit II

#include<bits/stdc++.h>
using namespace std;
 
#define debug(x) cout << #x << " = " << x << "\n"
#define pb push_back
 
typedef long long ll;
typedef vector<ll> vi;
typedef pair<ll,ll> pi;
 
const ll M = 1000000007;
const ll INF = LLONG_MAX/2-1;
 
ll g[2004][2004]; 
void triangle(){
    g[2][1] = 1;
    for(int i=2; i<=2001; i++){
        for(int r=0; r<=i; r++){
            g[i+1][r] = ((r*g[i][r]%M + (i+1-r)*g[i][r-1]%M)%M + i*g[i-1][r-1]%M)%M; 
        }
    }
}

vi fact(2002);
void factorials(){
    int sol=1;
    for(int i=2; i<2002; i++){
        fact[i-1] = sol;
        sol = ((sol%M)*i)%M;
    }
}


vector<vi> comb;
vector<vi> calcom(int n) {
    vector<vi> nCr(n + 1, vi(n + 1, 0));
    for (int i = 0; i <= n; i++) {
        nCr[i][0] = 1;
        nCr[i][i] = 1; 
    }
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j < i; j++) {
            nCr[i][j] = (nCr[i - 1][j - 1] + nCr[i - 1][j]) % M;
        }
    }
    return nCr;
}



void solve(){
    int n,a,b; cin >> n >> a >> b;
    if(a+b>n || ((a==0)^(b==0))){
        cout << 0 << "\n";
    }else if(a==0 && b==0){
        cout << fact[n] << "\n";
    }else{
        cout << ((comb[n][n-a-b]%M * g[a+b][a]%M)%M * fact[n]%M)%M << "\n";
    }
}
 
int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
 
    int t=1; cin >> t;
    triangle();
    factorials();
    comb = calcom(2002);

    while(t--) solve();
 
    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