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 MOD (long long)(1e9+7)
using namespace std;
long long n,k,dp[100005],c[105],sum[100005];
int main()
{
	cin >> n >> k;
	for(int i=1; i<=n; i++) cin >> c[i];
	dp[0]=sum[0]=1;
	for(int i=1; i<=n; i++)
	{
		for(int j=1; j<=k; j++) sum[j]=(dp[j]+sum[j-1]);
		for(int j=1; j<=k; j++) dp[j]=(sum[j]-(j<=c[i]?0:sum[j-c[i]-1]))%MOD;
	}
	//for(int j=0; j<=k; j++) cout << sum[j] << ' ';cout<<'\n';
	cout << dp[k];
	return 0;
}