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 N=1e5+5,zqm=1e9+7;
int f[N],pre[N];

int sum(int l,int r) {return (pre[r]-(l<=0 ? 0 : pre[l-1])+zqm)%zqm;}

int main() {
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
	
	int n,k; scanf("%d%d",&n,&k);
	f[0]=1,fill(pre,pre+k+1,1);
	for(int i=1,a;i<=n;++i) {
		scanf("%d",&a);
		for(int j=1;j<=k;++j) f[j]=sum(j-a,j);
		for(int j=1;j<=k;++j) pre[j]=(pre[j-1]+f[j])%zqm;
	}
	printf("%d\n",f[k]);
	
	return 0;
}
