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;
typedef long long ll;

const int M = 1e9+7;
ll n, k, bd[101][200001], a;

int main() {
	cin >> n >> k;
	memset(bd, 0, sizeof(bd));
	bd[0][k] = 1;
	for (int i=1; i<=n; i++) {
		cin >> a;
		bd[i][k] = 1;
		for (int j=k-1; j>=0; j--) {
			bd[i][j] = (bd[i][j+1]-bd[i-1][j+a+1]+bd[i-1][j]+M)%M;	
		}
	}
	cout << bd[n][0] << "\n";
}