Subset Fight

#include <bits/stdc++.h>
#define LL long long int
#define PB push_back
#define PF push_front
#define N 100005
#define INF 1000000000
using namespace std;
int n,v[105];
const int M=1e9+7;
LL fact[200005],invfact[200005],dp[105];

LL lgpow(LL a,LL p)
{
    LL val=1,x=a%M;
    while(p>0)
        if(p%2==0)
        {
            x=x*x%M;
            p/=2;
        }
        else
        {
            val=val*x%M;
            p--;
        }
    return val;
}

int main()
{
    cin>>n;
    for(int i=1;i<=n;++i)
        cin>>v[i];
    fact[0]=1;
    for(int i=1;i<=200000;++i)
        fact[i]=(1LL*fact[i-1]*i)%M,invfact[i]=lgpow(fact[i],M-2);
    invfact[0]=1;
    dp[0]=1;
    for(int i=1;i<=n;++i)
    {
        vector<LL> dp2(n+5,0),newdp(n+5,0);
        for(int j=1;j<=v[i];++j)
        {
            int p=(i*j)%n;
            LL jos=1LL*(invfact[j]*invfact[v[i]-j])%M;
            dp2[p]=(dp2[p]+(1LL*fact[v[i]]*jos)%M)%M;
        }
        for(int j=0;j<n;++j)
        {
            for(int d=0;d<n;++d)
            {
                int r=(j-d+n)%n;
                newdp[j]=(newdp[j]+(1LL*dp[d]*dp2[r])%M)%M;
            }
        }
        for(int j=0;j<n;++j)
            dp[j]=(dp[j]+newdp[j])%M;
    }
    cout<<dp[0];
    return 0;
}