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;
#define int int64_t
int a[102],dp[102][100004],s[102][100005];
signed main()
{
	int n,i,j,k,w=0,t;
	cin>>n>>k;
	for(i=1;i<=n;i++)
	cin>>a[i];
	dp[0][0]=1;
	for(i=1;i<=k+1;i++)
	s[0][i]=1;
	for(i=1;i<=n;i++)
	for(j=0;j<=k;j++)
	{   
	    int v=s[i-1][j+1]-s[i-1][max(w,j-a[i])];
	    if(v<0)
	    v=v+1000000007;
	    dp[i][j]=(v+dp[i][j])%1000000007;
	    s[i][j+1]=(s[i][j]+dp[i][j])%1000000007;
	    
	}
	cout<<dp[n][k]<<"\n";
}