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 maxn = 110, maxm = 1e5 + 10, P = 1e9 + 7;
int n, k, s[maxm], f[maxn][maxm];

int main() {
	scanf("%d %d", &n, &k), f[0][0] = 1;
	for (int i = 1, x; i <= n; i++) {
		scanf("%d", &x), s[0] = f[i - 1][0];
		for (int j = 1; j <= k; j++) {
			s[j] = (s[j - 1] + f[i - 1][j]) % P;
		}
		for (int j = 0; j <= k; j++) {
			f[i][j] = (s[j] - (j - x > 0 ? s[j - x - 1] : 0) + P) % P;
		}
	}
	printf("%d", f[n][k]);
	return 0;
}