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>
#include <vector>

using namespace std;

#define MOD 1000000007

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

	return 0;
}