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 P 1000000007
#define ll long long
#define ld long double
#define N (1<<17)
#define pii pair<int, int>
#define F first
#define S second

using namespace std;

int n, k;
int a[101];
ll d[101][2*N];

int main(){

	cin >> n >> k;

	for(int i=1; i<=n; i++) cin >> a[i];

	d[0][k]++;

	for(int i=1; i<=n; i++){
		for(int j=0; j<=a[i]; j++) d[i][0] = (d[i][0]+d[i-1][j])%P;
		for(int j=1; j<=k; j++){
			d[i][j] = (d[i][j-1]-d[i-1][j-1]+d[i-1][j+a[i]]+P)%P;
		}
	}

	cout << d[n][0] << endl;

	return 0;

}
