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 mod=(int)1e9+7;
const int maxk=(int)1e5+10;
int dp[maxk];
int prze[maxk];

int main()
{
	int n,k;
	scanf("%d %d",&n, &k);
	for(int i=0;i<=k;i++)
		dp[i]=1;
	prze[0]=1;
	while(n--)
	{
		int a;
		scanf("%d",&a);
		for(int i=1;i<=k;i++)
			prze[i]=(dp[i]-((i-a-1<0) ? 0 : dp[i-a-1]))%mod;
		for(int i=1;i<=k;i++)
			dp[i]=(prze[i]+dp[i-1])%mod;
	}
	printf("%d",(dp[k]-dp[k-1]+mod)%mod);
}