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<cstdio>
#include<algorithm>
using namespace std;
int n, w[3010], K, D[110][101000], Mod = 1000000007, S[101000];
int main() {
	int i, j, k, a;
	scanf("%d%d", &n,&K);
	D[0][0] = 1;
	for (i = 1; i <= n; i++) {
		scanf("%d", &a);
		for (j = 0; j <= K; j++) {
			S[j + 1] = (S[j] + D[i - 1][j]) % Mod;
		}
		for (j = 0; j <= K; j++) {
			D[i][j] = (S[j + 1] - S[max(0, j - a)] + Mod) % Mod;
		}
	}
	printf("%d\n", D[n][K]);
}