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 maxn=100005;
const int mod=1e9+7;

int n,k,a[maxn],dp[105][maxn];

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