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;

const int P=1e9+7;

int n,K;
int a[100010];
int f[102][100002];
int sum[102][100002];

int main(){
	scanf("%d%d",&n,&K);
	for(int i=1;i<=n;i++){
		scanf("%d",a+i);
	}
	for(int i=0;i<=K;i++)
		f[0][i]=sum[0][i]=1;
	for(int i=1;i<=n;i++){
		for(int j=0;j<=K;j++){
			f[i][j]=((sum[i-1][j]-((j-a[i]-1)>=0?sum[i-1][j-a[i]-1]:0))%P+P)%P;
			sum[i][j]=((j==0?0:sum[i][j-1])+f[i][j])%P;
		}
	}
	printf("%d\n",f[n][K]);

	return 0;
}