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 ll long long
using namespace std;
const int mod=1e9+7;
ll n,a[101],f[101][100010],k,sum[101][100010];
int main()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	f[0][0]=1;
	for(int i=0;i<=k;i++)
		sum[0][i]=sum[0][i-1]+f[0][i];
	for(int i=1;i<=n;i++)
	{
		for(int j=0;j<=k;j++)
		{
			f[i][j]=(sum[i-1][j]+mod-sum[i-1][j-min((ll)j,a[i])-1])%mod;
			sum[i][j]=(f[i][j]+sum[i][j-1])%mod; 
		}
	}
	cout<<f[n][k]<<endl;
	return 0;
}
