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 mod = 1e9 + 7;
int n, a[110], k;
long long dp[110][100100];

int main() {
	cin >> n >> k;
	for (int i = 0; i < n; i++) cin >> a[i];
	
	dp[0][0] = 1;
	for (int i = 0; i < n; i++) {
		for (int j = 1; j <= k; j++) {
			dp[i][j] = (dp[i][j] + dp[i][j - 1]) % mod;
		}
		for (int j = 0; j <= k; j++) {
			dp[i + 1][j] = dp[i][j];
			if (j - a[i] - 1 >= 0) dp[i + 1][j] += mod - dp[i][j - a[i] - 1];
			dp[i + 1][j] %= mod;
		}
	}
	
	cout << dp[n][k] << '\n';
}
