There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
#include <bits/stdc++.h>
using namespace std;
long long dp[110][100010],sum[100010];
const int MAXN=1e9+7;
int n,k,a[100010];
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;++i){
		cin>>a[i];
		dp[i][0]=1;
	}
	dp[0][0]=1;
	for(int i=1;i<=n;++i){
		for(int j=1;j<=k+1;++j){
			sum[j]=sum[j-1]+dp[i-1][j-1];
			sum[j]%=MAXN;
		}
		for(int j=1;j<=k;++j){
			dp[i][j]=sum[j+1]-sum[max(0,j-a[i])]+MAXN;
			dp[i][j]%=MAXN;
		}
	}
	/*for(int i=1;i<=n;++i){
		for(int j=0;j<=k;++j){
			cout<<dp[i][j]<<" ";
		}
		cout<<endl;
	}*/
	cout<<dp[n][k]%MAXN<<endl;
	return 0;
}
