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

int M=1e9+7;

signed main() {
	int N,K;
	cin>>N>>K;
	vector<int> candies(N+1);
	for (int i=0;i<N;i++){
		cin>>candies[i];
	}
	vector<int>dp(K+1);
	dp[0]=1;
	for (int i=1;i<=N;i++){
		vector<int> prefix_sum(K+1);
		prefix_sum[0]=dp[0];
		for (int j=1;j<=K;j++){
			prefix_sum[j]=(prefix_sum[j-1]%M+dp[j]%M)%M;
		}
		for (int j=K;j>=0;j--){
			if (j<=candies[i-1]) dp[j]=prefix_sum[j];
			else dp[j] = (M+prefix_sum[j]-prefix_sum[j-candies[i-1]-1])%M;
		}
	}
	cout<<dp[K];
    return 0; 
}
