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 f[110][100010],n,k,a[110],sum[110],mode=1000000007,sum1[100010];
int main()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
		sum[i]=sum[i-1]+a[i];
	}
	for(int i=0;i<=a[1];i++)
		f[1][i]=1;
	for(int i=2;i<=n;i++)
	{
		for(int j=0;j<=k;j++)
			sum1[j]=(sum1[j-1]+f[i-1][j])%mode;
		for(int j=0;j<=min(sum[i],k);j++)
		{
			f[i][j]=((sum1[min(j,sum[i-1])]-sum1[max(0,j-a[i])-1]))%mode;
			if(f[i][j]<0)
				f[i][j]+=mode;
		}
	}
	cout<<f[n][k]%mode<<endl;
	return 0;
}
