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 <iostream>
#include <vector>
using namespace std;
const long long nin = 1e9 + 7;

int main()
{
	int n, k;
	cin >> n >> k;
	long long a[n + 1], ans[k + 1];
	vector <long long> sum (k + 1, 1);
	for (int i = 1; i <= n; i++)
		cin >> a[i];
	
	sum[0] = 1;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 0; j <= k; j++)
			if (j > a[i]) 
			{
				ans[j] = (sum[j] - sum[j - a[i] - 1]) % nin;
				if (ans[j] < 0) ans[j] += nin;
			}
			else ans[j] = sum[j];
		
		for (int j = 1; j <= k; j++)
			sum[j] = (sum[j - 1] + ans[j]) % nin;
	}
	
	cout << ans[k];
}