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;
typedef long long LL;
const LL MOD=1e9+7;
int n,k,a[102];
LL dp[102][100002];
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	dp[0][0]=1;
	for(int i=1;i<=n;i++){
		LL s[100002]={0};
		s[0]=dp[i-1][0];
		for(int j=1;j<=k;j++)s[j]=(s[j-1]+dp[i-1][j])%MOD;
		for(int j=0;j<=k;j++){
			int r=j,l=max(0,j-a[i]);
			dp[i][j]=s[r]-(l>=1?s[l-1]:0);
		}
	}
	cout<<(dp[n][k]%MOD+MOD)%MOD<<endl;
}