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;

int main()
{
	long long int  n,k,mod=1000000007;;
	long long int vect[110];
	static long long int dp[110][100010]={};
	cin>>n>>k;
	for(int i=0;i<n;i++)
	cin>>vect[i];
	dp[0][0]=1;
	for(int i=0;i<n;i++)
	{
		static long long int sum[100010]={};
		for(int j=0;j<=k;j++)
		{
			sum[j+1]=(sum[j]+dp[i][j])%mod;
		}

		for(int j=0;j<=k;j++)
		{
			dp[i+1][j]=(sum[j+1]-sum[max(0LL,j-vect[i])]+mod)%mod;
		}
	}
	cout<<dp[n][k];


	return 0;
}