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;

const int MOD = 1000000007;

void add(int &a, int b) { a += b; if(MOD <= a) a -= MOD; }
void sub(int &a, int b) { a -= b; if(a < 0) a += MOD; }

int dp[2][100055];

int N, K;

int main() {
	cin >> N >> K; dp[0][0] = 1;
	for(int ni = 0, a; ni < N; ni++) {
		cin >> a;
		for(int i = 0, j = -a, s = 0; i <= K; i++, j++) {
			add(s, dp[0][i]);
			dp[1][i] = s;
			if(0 <= j) sub(s, dp[0][j]);
		}
		memcpy(dp[0], dp[1], (K+1) * sizeof(int));
	}
	cout << dp[0][K] << endl;
	return 0;
}