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;
const int p = 1e9 + 7;
int main(){
	int n,k; cin >> n >> k;
	vector<int> dp(k+1); dp[0] = 1;
	for(int i = 0; i < n; i++){
		int c; cin >> c;
		vector<int> pfx(k+1);
		for(int cur = k; cur >= 0; cur--){
			int rb = min(k - cur, c);
			if(rb < 1) continue;
			(pfx[cur + 1] += dp[cur]) %= p;
			if(cur + rb + 1 <= k) (pfx[cur + rb + 1] -= dp[cur] - p) %= p;
		}
		for(int i = 1; i <= k; i++) (pfx[i] += pfx[i-1]) %= p, (dp[i] += pfx[i]) %= p;
	}
	cout << dp[k] << endl;
}