Kortit II

#include<bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0;i<n;++i)
#define forN(i,k,n) for(int i=k;i<n;++i)
#define pb push_back
#define F first
#define S second
#define all(x) (x.begin()),(x.end())
#define rall(x) (x.rbegin()),(x.rend())
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define inf ((int)(1.01e9))
#define mod ((int)(1e9+7))
#define N ((int)(101))
 
ll n, m, a, b;
 
ll arr[N+2][N+2][N+2], fact[N+2];
 
ll rev(ll a, ll m) {
    if (a==1) return 1;
    return (1-rev(m%a, a)*m) / a + m;
}
 
ll nCr(ll n, ll r) {
    if (!r) return 1;
    return (fact[n]%mod * rev(fact[r], mod)%mod * rev(fact[n-r], mod)%mod)%mod;
}
 
void solve() {
    cin >> m >> a >> b;
    if (m < a + b || ((!b)&&a) || ((!a)&&b)) {
        cout << "0" << endl;
        return;
    }
    if (a > b) swap(a,b);
    n = a + b;
    
    ll comb = nCr(m,m-n);
    comb = comb * comb % mod * fact[m-n] % mod * fact[n] % mod; 
 
    int counter = arr[n+1][a][b];
    if (!counter) counter=1;
    int result = (counter*comb) % mod;
    cout << result << endl;
}
 
int main() {
    cin.tie(0) -> sync_with_stdio(0);
    cout.tie(0);
    fact[0] = fact[1] = 1;
    forN(i,2,N) fact[i] = (i)*fact[i-1] % mod; 
 
    memset(arr, 0, sizeof(arr));
 
    arr[1][0][0] = 1;
 
    for(int i = 1; i < N; i++) {
        for(int A = 0; A < i; A++) {
            for(int B = 0; B < i && B+A < i; B++) {
                ll f = i-1 - A - B;
                // a, b, f+1
                arr[i+1][A][B] = (arr[i+1][A][B] + arr[i][A][B]) % mod;
                if (!f) continue;
                // a+1, b, f
                arr[i+1][A+1][B] = (arr[i+1][A+1][B] + f * arr[i][A][B] % mod) % mod;
                // a, b+1, f
                arr[i+1][A][B+1] = (arr[i+1][A][B+1] + f * arr[i][A][B] % mod) % mod;
                // a+1, b+1, f-1
                arr[i+1][A+1][B+1] = (arr[i+1][A+1][B+1] + f*f%mod * arr[i][A][B]%mod) % mod;
            }
        }
    }
 
    int t;
    cin >> t;
    while(t--) solve();
}

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: RUNTIME ERROR

Test 6

Group: 5

Verdict: RUNTIME ERROR