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 fish=1e9+7;
int N,a[505],K;
long long dp[205][100005];
long long Sum[100005];
int main()
{
	scanf("%d%d",&N,&K);
	for (int i=1;i<=N;i++)
	 scanf("%d",&a[i]);
	for (int i=0;i<=N;i++)
	  dp[i][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];
	    for (int j=1;j<=K;j++)
	      dp[i][j]=dp[i][j]+Sum[j+1]-Sum[max(0ll,j*1ll-a[i])],dp[i][j]%=fish;
	}
	printf("%d",dp[N][K]);
	return 0;
}