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 maxk=1e5+5, maxn=105, mod=1e9+7;

int dp[maxn][maxk];

inline int sum(int a, int b){
	if(a+b>=mod){
		return a+b-mod;
	}
	else if(a+b<0){
		return a+b+mod;
	}
	return a+b;
}

int main(){
	int n, k;
	scanf("%d%d", &n, &k);
	int a;
	dp[0][0]=1;
	int suma;
	for(int i=0; i<n; i++){
		scanf("%d", &a);
		suma=0;
		for(int j=0; j<=k; j++){
			suma=sum(suma, dp[i][j]);
			if(j-a>0){
				suma=sum(suma, -dp[i][j-a-1]);
			}
			dp[i+1][j]=suma;
		}
	}
	printf("%d\n", dp[n][k]);
	return 0;
}