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>

#define ll long long

using namespace std;

int mod = (int)1e9 + 7;

int add(int a, int b) {
	return (a + b) % mod;
}

int dp[101][(int)1e5 + 1];
int n, k;

int main() {
	scanf("%d %d", &n, &k);
	dp[0][k] = 1;
	for (int i = 1, x; i <= n; i++) {
		scanf("%d", &x);
		int cur = 0;
		for (int j = k; j >= 0; j--) {
			cur = add(cur, dp[i - 1][j]);
			if (j + x + 1 <= k) {
				cur = add(cur, mod - dp[i - 1][j + x + 1]);
			} 
			dp[i][j] = cur;
		}
	}
	cout << dp[n][0];
}
