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 dp[105][100005],n,m,val[105];
int main()
{
	scanf("%d %d",&n,&m);
	for(int i=1;i<=n;i++)scanf("%d",&val[i]);
	for(int j=m;j>-1;j--)
	{
		if(j>=m-val[1])dp[1][j]=1;
		else dp[1][j]=0;
	}
	for(int i=2;i<=n;i++)
	{
		long long k=0;
		for(int j=m;j>-1;j--)
		{
			if(j<m-val[i])k-=dp[i-1][j+val[i]+1];
			k+=dp[i-1][j];
			k+=1000000007;
			k%=1000000007;
			dp[i][j]=k;
		}
	}
	printf("%d",dp[n][0]);
}