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;

#define REP(i,n) for(int (i)=0; i<(int)(n); i++)

int dp[101][100100];

int main(void) {
	int N,K;
	cin >> N >> K;
	dp[0][0] = 1;
	REP(i,N) {
		int x;
		cin >> x;
		int sum=0;
		for(int j=0; j<=K; j++) {
			sum = (sum+dp[i][j]) % 1000000007;
			if(j > x)
				sum = (sum+1000000007-dp[i][j-x-1]) % 1000000007;
			dp[i+1][j] = sum;
		}
	}
	cout << dp[N][K] << endl;
	return 0;
}
