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;
#define MOD 1000000007
int n, k;
int a[110];
long long dp[110][100010];
int main () {
	cin >> n >> k;
	for (int i=1; i<=n; i++) {
		cin >> a[i];
	}
	dp[0][0] = 1;
	for (int i=1; i<=n; i++) {
		dp[i][0] = 1;
		for (int j=1; j<=k; j++) {
			dp[i][j] = (dp[i][j-1]+dp[i-1][j])%MOD;
			if (j-a[i]-1 >= 0) dp[i][j] = (MOD+dp[i][j]-dp[i-1][j-a[i]-1])%MOD;
		}
	}
	cout << dp[n][k] << endl;
}