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 MAXN=110,MAXK=100010;
const long long M=1e9+7;
int n,k,a[MAXN];
long long s[MAXK],dp[MAXN][MAXK];

int main(){
	cin>>n>>k,dp[0][0]=1;
	for(int i=1;i<=n;cin>>a[i],dp[i][0]=1,++i);
	for(int i=1;i<=n;++i){
		for(int j=1;j<=k+1;++j) (s[j]=s[j-1]+dp[i-1][j-1])%=M;
		for(int j=1;j<=k;++j) (dp[i][j]=s[j+1]-s[max(0,j-a[i])]+M)%=M;
	}
	cout<<dp[n][k]<<endl;
	return 0;
}