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 <cstdio>
#include <cstring>
int S[100001],dp[101][100001],n,k,a[100001],c;const int p=1e9+7;
int &s(int x){if(x<0)return c;else return S[x];}
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)s(i)=1;
	for(int i=1;i<=n;++i)
	{
		for(int j=0;j<=k;++j)dp[i][j]=((s(j)-s(j-a[i]-1))%p+p)%p;
		for(int j=0;j<=k;++j)s(j)=(s(j-1)+dp[i][j])%p;
	}
	printf("%d\n",dp[n][k]);
}