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;

void solve()
{
	int N, K, a;
	cin >> N >> K;
	vector<long> dp(K+1);
	dp[0] = 1;
	for (int i = 0; i < N; i++)
	{
		cin >> a;
		vector<long> nx = dp;
		for (int j = 1; j <= K; j++)
		{
			if (j > a)
			{
				(nx[j] += nx[j-1] - dp[j-a-1] + MOD) %= MOD;
			}
			else
			{
				(nx[j] += nx[j-1]) %= MOD;
			}
		}
		dp = nx;
	}

	cout << dp[K] << endl;
}

int main()
{
	solve();
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}
