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>
#define ll long long
#define MOD 1000000007
using namespace std;

int main()
{
	int n, K;
	cin >> n >> K;

	int a[n];
	for (int i = 0; i < n; ++i)
		cin >> a[i];

	ll dp[n][K+1];
	memset(dp, 0, sizeof(dp));
	for (int i = 0; i < K+1 and a[0] >= i; ++i)
		dp[0][i] = 1;

	for (int i = 1; i < n; ++i)
	{
		ll sum = 0;
		for (int j = 0; j <= K; ++j)
		{
			if(j-a[i]-1 >= 0)
				sum = (sum - dp[i-1][j-a[i]-1] + MOD)%MOD;
			sum = (sum + dp[i-1][j])%MOD;

			dp[i][j] = (dp[i][j] + sum)%MOD;
		}
	}
	
	cout << dp[n-1][K];
	return 0;
}