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;

long d[111111] = { 1 };
int main() {
	int n, k, p = 1e9 + 7;
	cin >> n >> k;
	for (int i = 0; i < n; i++) {
		int a;
		cin >> a;
		partial_sum(d, d + k + 1, d);
		for (int j = k - a; j--;)
			d[j + a + 1] -= d[j];
		for (int j = 0; j < k; j++)
			d[j + 1] %= p;
	}
	cout << d[k] << endl;
	return 0;
}
