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<iostream>
using namespace std;
const int mod=1e9+7;
void candies(int n,int a[],int k){
	long long int way[n][k+1];
	for(int i=0;i<=a[0];i++)
	way[0][i]=1;
	for(int i=a[0]+1;i<k+1;i++)
	way[0][i]=0;
	for(int i=1;i<n;i++){
		way[i][0]=1;
		for(int j=1;j<k+1;j++){
			if(j<=a[i])
			way[i][j]=(way[i-1][j]+way[i][j-1])%mod;
			else
			way[i][j]=(way[i][j-1]-way[i-1][j-a[i]-1]+way[i-1][j]+mod)%mod;
		}
	}
	cout<<way[n-1][k]<<endl;
}
int main(){
	int n,k;cin>>n>>k;
	int a[n];
	for(int i=0;i<n;i++)
	cin>>a[i];
	candies(n,a,k);
}