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 MOD 1000000007LL

long long dp[110][101010];

int main(){
	int N,K;
	cin >> N >> K;
	vector<int> a(N);
	for(auto &i:a)cin >> i;
	
	dp[0][0]=1;
	
	for(int i=0;i<N;i++){
		for(int j=0;j<=K;j++){
			dp[i+1][j]+=dp[i][j];
			dp[i+1][j]%=MOD;
			dp[i+1][min(j+a[i],K)+1]+=MOD-dp[i][j];
			dp[i+1][min(j+a[i],K)+1]%=MOD;
		}
		for(int j=0;j<K;j++){
			dp[i+1][j+1]+=dp[i+1][j];
			dp[i+1][j+1]%=MOD;
		}
	}
	cout << dp[N][K] << endl;
	return 0;
}