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>
const int N=103,M=1e9+7;
inline int Mod(int a){return a<M?a:a-M;}
int n,m,a[N],f[N][100003];
signed main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	for(int j=0;j<=m;j++)f[0][j]=1;
	for(int i=1;i<=n;i++)
	  for(int j=0;j<=m;j++)
		f[i][j]=Mod((j>0?f[i][j-1]:0)+Mod(f[i-1][j]-(j-a[i]-1<0?0:f[i-1][j-a[i]-1])+M));
	printf("%d",Mod(f[n][m]-(m>0?f[n][m-1]:0)+M));
	return 0;
}