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 MOD 1000000007
int main() {
	int n, k;
	cin>>n>>k;
	int arr[n];
	for(int i=0;i<n;i++){
	    cin>>arr[i];
	}
	int dp[n+1][k+1];
	dp[0][0] = 1;
	for(int i=1;i<=k;i++){
	    dp[0][i] = 0;
	}
	for(int i=1;i<=n;i++){
	    for(int j=0;j<=k;j++){
	        if(j == 0){
	            dp[i][j] = dp[i-1][j];
	        }else{
	            dp[i][j] = ((dp[i-1][j] + dp[i][j-1])%MOD - ((j-1-arr[i-1] >= 0) ? dp[i-1][j-1-arr[i-1]] : 0) + MOD)%MOD;
	        }
	    }
	}
	cout<<dp[n][k];
	return 0;
}