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<iostream>
using namespace std;
const int mod=1e9+7;
int a[101];
int dp[100001][101];
int qzh[100001][101];
int main()
{
	int n,k;cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	qzh[0][0]=dp[0][0]=1;
	for(int i=1;i<=k;i++)
		qzh[i][0]=qzh[i-1][0]+dp[i][0];
	for(int i=1;i<=n;i++)
		qzh[0][i]=dp[0][i]=1;
	for(int i=1;i<=k;i++)
		for(int j=1;j<=n;j++)
		{
			dp[i][j]=(qzh[i][j-1]-((i-a[j]>0)?qzh[i-a[j]-1][j-1]:0))%mod;
			qzh[i][j]=(qzh[i-1][j]+dp[i][j])%mod;
		}
	cout<<(dp[k][n]+mod)%mod;
	return 0;
}