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>
#define mod 1000000007
using namespace std;
int n,a[105],dp[100005],qzh[100005],k;
int main(int argc, char** argv) {
	cin >> n >> k;
	for(int i=1;i<=n;i++)
		cin >> a[i];
	qzh[k]=1;
	for(int i=1;i<=n;i++)
	{
		for(int j=0;j<=k;j++)
		{
			dp[j]=qzh[min(k,j+a[i])];
			if(j>0) dp[j]-=qzh[j-1];
			dp[j]%=mod,dp[j]+=mod,dp[j]%=mod;
		}
		qzh[0]=dp[0];
		for(int j=1;j<=k;j++) qzh[j]=(dp[j]+qzh[j-1])%mod;
	}
	cout << dp[0];
	return 0;
}