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 N = 1e5 + 100, MODD = 1e9 + 7;
 
int dp[N], par_sum[N];
 
int main() {
	int n, k, a;
	cin >> n >> k;
	dp[0] = 1;
	for (int i = 1; i <= n; ++i) {
		for (int j = 0; j <= k; ++j) {
                        par_sum[j + 1] = par_sum[j] + dp[j];
                        par_sum[j + 1] %= MODD;
                }
		cin >> a;
		for (int j = 0; j <= k; ++j) {
			dp[j] = par_sum[j + 1];
			if (j - a >= 1)
				dp[j] -= par_sum[j - a];
			if (dp[j] < 0)
				dp[j] += MODD;
		}
	}
	cout << dp[k] << '\n';
}
