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;
int dp[105][100005],a[105],n,k;
const int MOD=1e9+7;
int main()
{
	cin>>n>>k;
	for(int i=0;i<n;i++)
		cin>>a[i];
	for(int i=0;i<=a[0];i++)
		dp[0][i]=1;
	for(int i=1;i<n;i++)
	{
		vector<int>vec(k+1);
		vec[0]=dp[i-1][0];
		for(int j=1;j<k+1;j++)
			vec[j]=(vec[j-1]+dp[i-1][j])%MOD;
		for(int j=0;j<k+1;j++)
		{
			if(j>a[i])
				dp[i][j]=(vec[j]+MOD-vec[j-a[i]-1])%MOD;
			else
				dp[i][j]=vec[j];
		}
	}
	cout<<dp[n-1][k];
	return 0;
}