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<iostream>
using namespace std;
int n,k,a,i;
long dp[111][2<<17],mod=1e9+7;
int main()
{
	cin>>n>>k;
	dp[0][k]=1;
	for(;cin>>a;i++)
	{
		for(int j=k;j>=0;j--)
		{
			(dp[i+1][j]=dp[i][j]+dp[i+1][j+1]-dp[i][j+a+1]+mod)%=mod;
		}
	}
	cout<<dp[i][0]<<endl;
}