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 vll = std::vector<long long>;
constexpr long long mod{1000000007};

int main()
{
	int n, k;
	scanf("%d%d", &n, &k);
	std::vector<vll> combi(n + 1, vll(k + 1));
	combi[0][0] = 1;
	for (int n_i{1}; n_i <= n; n_i++)
	{
		int a;
		scanf("%d", &a);
		long long sum{};
		for (int k_i{}; k_i <= k; k_i++)
		{
			sum += combi[n_i - 1][k_i];
			sum %= mod;
			if (k_i - a - 1 >= 0)
			{
				sum += mod - combi[n_i - 1][k_i - a - 1];
				sum %= mod;
			}
			combi[n_i][k_i] = sum;
		}
	}
	printf("%lld\n", combi[n][k]);

	return 0;
}