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 mp make_pair
#define pb push_back
#define fi first
#define se second

int n, k, a[107], dp[107][200007];
const int mod = 1e9 + 7;

int main(){
	ios_base::sync_with_stdio(0); cin.tie(0);
	cin >> n >> k;
	dp[0][k] = 1;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
		int r = k, sum = 0;
		for(int j = k; j >= 0; j--){
			sum += dp[i - 1][j];
			if(sum >= mod) sum -= mod;
			sum = sum - dp[i - 1][j + a[i] + 1] + mod;
			sum %= mod;
			dp[i][j] = sum;
		}
	}
	cout << dp[n][0];
}
