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"
using namespace std;

int main() {
	long long N, K, A[100], MOD = 1000000007;
	static long long DP[110][100010] = {};
	DP[0][0] = 1;
	cin >> N >> K;
	for (int i = 0; i < N; i++) cin >> A[i];
	for (int i = 0; i < N; i++) {
		static long long SUM[100010] = {};
		for (int j = 0; j <= K; j++) {
			SUM[j + 1] = (SUM[j] + DP[i][j]) % MOD;
		}
		for (int j = 0; j <= K; j++) {
			DP[i + 1][j] = (SUM[j + 1] - SUM[max(0LL, j - A[i])] + MOD) % MOD;
		}
	}
	cout << DP[N][K] << endl;
}