This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define vi vector<int>
#define pb push_back
#define ll long long
#define F first
#define S second
#define mp make_pair
#define ii pair<int,int>
#define fast ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
const ll MOD=1e9+7;
int n,l,x;
const int tam=10005;
ll fact[50005];
void init(){
fact[0]=1;
for(int i=1;i<=50000;i++){
fact[i]=(fact[i-1]*i)%MOD;
}
}
ll Pou(int a, int n){
if(n==0)return 1;
if(n%2==0){
ll A=Pou(a,n/2);
return (A*A)%MOD;
}else{
ll A=Pou(a,n/2);
A=(A*A)%MOD;
return (A*a)%MOD;
}
}
ll nck(int n, int k){
ll res=(fact[n]*Pou((fact[k]*fact[n-k])%MOD,MOD-2))%MOD;
return res;
}
int main(){
init();
cin>>n>>l;
for(int i=0;i<n;i++){
cin>>x;
}
ll libre=l-(n-1)*x-1;
if(libre<0){
cout<<0<<endl;
return 0;
}
cout<<nck(n+libre,n)*fact[n]%MOD<<endl;
return 0;
}
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