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>
using namespace std;

int n, k, a;
int dp[101][1000001];
int pr[101][1000001];

int main()
{
	cin >> n >> k;
	
	dp[0][0] = 1;
	for(int j = 0; j <= k; j++)
	pr[0][j] = 1;
	
	for(int i = 1; i <= n; i++)
	{
		cin >> a;
		dp[i][0] = 1;
		pr[i][0] = 1;
		for(int j = 1; j <= k; j++)
		{
			dp[i][j] = pr[i - 1][j];
			if(j - a - 1 >= 0)
				dp[i][j] = (dp[i][j] - pr[i - 1][j - a - 1] + int(1e9 + 7)) % int(1e9 + 7);
			pr[i][j] = (pr[i][j - 1] + dp[i][j]) % int(1e9 + 7);
		}
	}
	
	cout << dp[n][k] << endl;
}
