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 MOD (int)(1e9+7)

using namespace std;

long long mem[2][100005];
int n,k;
int arr[105];

int main()
{
	cin >> n >> k;
	for(int i=0;i<n;i++)
		cin >> arr[i];
	mem[n%2][0]=1;
	for(int i=n-1;i>=0;i--)
	{

		for(int j=1;j<=k;j++){
			mem[1-i%2][j]+=mem[1-i%2][j-1];
			mem[1-i%2][j]%=MOD;
		}
		for(int j=0;j<=k;j++)
		{
			// j-arr[i],j
			mem[i%2][j]=(mem[1-i%2][j]-(j-arr[i]>0?mem[1-i%2][j-arr[i]-1]:0)+MOD)%MOD;
		}
	}
	cout << mem[0][k] << endl;
}