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;

long long N, K, A[100009], dp[109][100009], mod = 1000000007;

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++) {
		for (int j = 1; j <= K; j++) { dp[i - 1][j] += dp[i - 1][j - 1]; dp[i - 1][j] %= mod; }
		for (int j = 0; j <= K; j++) {
			long long R = dp[i - 1][j];
			long long L = 0; if (j > A[i]) L = dp[i - 1][j - A[i] - 1];
			dp[i][j] = (R - L + mod) % mod;
		}
	}
	cout << dp[N][K] << endl;
	return 0;
}