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;

long dp[110][100010], mod=1000000007;
int main() {
	int N, K, a[110]; cin >> N >> K;
	for(int i=1; i<=N; ++i) cin >> a[i];
	dp[0][0]=1;
	for(int i=1; i<=N; ++i){
	    long ad=0;
	    for(int j=0; j<=K; ++j){
	        ad=(ad+dp[i-1][j])%mod;
	        dp[i][j]=ad;
	        if(j>=a[i]) ad=(ad+mod-dp[i-1][j-a[i]]);
	    }
	}
	cout << dp[N][K] << endl;
	return 0;
}
