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;

#define int long long

const int M = 1e9+7ll;

int n,m,a[105];
int f[105][100005],s[100005];

signed main()
{
	cin>>n>>m;
	for(int i=1;i<=n;cin>>a[i++]);
	f[0][0] = 1;
	for(int i=1;i<=n;i++)
	{
		memset(s,0,sizeof(s));
		s[0] = 1;
		for(int j=1;j<=m;j++)
			s[j] = s[j-1]+f[i-1][j];
		for(int j=0;j<=m;j++)
			if(j>a[i])
				f[i][j] = (s[j]-s[j-a[i]-1])%M;
			else
				f[i][j] = s[j]%M;
	}
	cout<<f[n][m]<<endl;
	
	return 0;
}