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;
int f[101][100001],a[100001];
int main()
{
	int i,n,j,k;
	scanf("%d%d",&n,&k);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
	f[0][0]=1;
	for(i=0;i<=k;i++)
		f[0][i]=1;
	for(i=1;i<=n;i++)
	{
		for(j=0;j<=k;j++)
		{
			f[i][j]=f[i-1][j];
			if(j-a[i]-1>=0)
				f[i][j]=(f[i][j]+1000000007-f[i-1][j-a[i]-1])%1000000007;
		}
		for(j=1;j<=k;j++)
			f[i][j]=(f[i][j]+f[i][j-1])%1000000007;
	}
	printf("%d",(f[n][k]-f[n][k-1]+1000000007)%1000000007);
	return 0;
}