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 main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	int N,K,mod=1e9+7;
	cin>>N>>K;
	vector<int>dp1(K+1,1),dp2(K+1);
	while(N--) {
		int a;
		cin>>a;
		for(int i=0;i<=K;i++) dp2[i]=(dp1[i]-(i-a-1>=0?dp1[i-a-1]:0)+mod)%mod;
		dp1[0]=dp2[0];
		for(int i=1;i<=K;i++) dp1[i]=(dp1[i-1]+dp2[i])%mod;
	}
	cout<<dp2[K]<<"\n";
	return 0;
}