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 LL long long

int N,K,a[100];
LL dp[101][100001] = {};
LL wa[101][100002] = {};
const LL MOD = 1000000007;

int main(){
	cin >> N >> K;
	for(int i=0; i<N; i++) cin >> a[i];

	dp[0][0] = 1;
	for(int i=0; i<=K; i++) wa[0][i+1] = 1;
	for(int i=1; i<=N; i++){
		for(int j=0; j<=K; j++){
			dp[i][j] = wa[i-1][j+1] - wa[i-1][max(0,j-a[i-1])] + MOD;
			dp[i][j] %= MOD;
			wa[i][j+1] = wa[i][j] + dp[i][j];
			wa[i][j+1] %= MOD;
		}
	}
	cout << dp[N][K] << endl;

	return 0;
}