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;

const int MAXN = 1e5 + 10, MD = 1e9 + 7;
int n, k, a[110];
ll dp[110][MAXN];

int main () {
	ios::sync_with_stdio(0), cin.tie(0);
	cout.tie(0);

	cin >> n >> k;
	for (int i = 1; i <= n; ++i) cin >> a[i];

	dp[0][0] = 1;
	for (int i = 1; i <= n; ++i) {
		ll ans = 0;
		for (int j = 0; j <= k; ++j) {
			ans += dp[i - 1][j];
			if(j - a[i] - 1 >= 0) ans -= dp[i-1][j - a[i] - 1];
			ans = (ans + MD) % MD;
			dp[i][j] = ans;
		}
	}

	cout << dp[n][k] << '\n';

	return 0;
}
