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 N=1e5+55;
ll sum[N];
ll dp[155][N];
ll mod=1e9+7;
int a[155];
int n,K;
	

int main()
{
	cin>>n>>K;
	for(int i=0;i<n;i++)
		cin>>a[i];
	dp[n][0]=1;
	for(int i=n-1;i>=0;i--)
	{
		sum[0]=dp[i+1][0];
		for(int k=1;k<=K;k++)
		{
			sum[k]=sum[k-1]+dp[i+1][k];
			sum[k]%=mod;
		}
		for(int k=0;k<=K;k++)
		{
			dp[i][k]=sum[k];
			if(a[i]<k)
			{
				dp[i][k]-=sum[k-a[i]-1];
				dp[i][k]+=mod;
				dp[i][k]%=mod;
			}
		}
	}
	cout<<dp[0][K]<<endl;
	
	return 0;
}
