Coloring scheme [SCOI2008] HYSBZ - 1079

https://vjudge.net/problem/HYSBZ-1079

#include<bits/stdc++.h>
using namespace std;
long long int C[100][100] = {}, A[20][100] = {};
const long long int mod = 1e9 + 7;
void init() {
    C[0][0] = 1;
    for (int i = 1; i < 90; ++i) {
        C[i][0] = C[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            C[i][j] = C[i][j] >= mod ? C[i][j] - mod : C[i][j];
        }
    }
}
long long int F(int x,int target, int t,int cnt) {
    long long int cnt0 = cnt - t,ans=0;
    for (int i = 0; i < t; ++i) {
        int tt = t - i,targett=target-i;
        if (targett <= x) ans+=  C[x][x - targett] * C[cnt0 - x][tt - (x - targett)] * C[t-1][i];
    }
    return ans;
}
int main() {
    init();
    int k,t;
    cin >> k;
    int cnt = 1;
    A[0][0] =1;
    for (int i = 1; i <= k;++i) {
        cin >> t;
        cnt += t;
        for (int j = 0; j <= cnt; ++j) {
            for (int idx = max(0,j-t); idx <= j + t; ++idx) {
                if(A[i-1][idx])
                    A[i][j] = (A[i][j]+A[i - 1][idx]*F(idx, j,t,cnt))%mod;
            }
            if (j == 0 && i == k) {
                cout << A[k][0];
                return 0;
            }
        }
    }
}