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