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>
#define pb push_back
using namespace std;
const int DN=105,DK=1e5+5,M=1e9+7;
int n,k,a[DN],dp[DN][DK],sum;
int main()
{
    cin>>n>>k;
    for(int i=1;i<=n;i++)
    	cin>>a[i];
    dp[0][0]=1;
    for(int i=1;i<=n;i++)
    {
    	sum=0;
    	a[i]++;
    	for(int j=0;j<=k;j++)
    	{
    		sum=(sum+dp[i-1][j])%M;
    		if(j>=a[i])
    			sum=(sum+M-dp[i-1][j-a[i]])%M;
    		dp[i][j]=sum;
    	}
    }
    cout<<dp[n][k];
}