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;
long long int dp[101][100001];

int main(){
long long int n,k;
cin>>n>>k;
long long int ar[n];
for(int i=0;i<n;i++)cin>>ar[i];
//memset(dp,1,sizeof(dp));

for(int i=0;i<n;i++)dp[i][0]=1;


for(int i=0;i<n;i++)for(int j=1;j<=k;j++)
{
if(i==0){if(j<=ar[i])dp[i][j]=1;
	else{  dp[i][j]=0;} }
	
else{
dp[i][j]=(dp[i-1][j]+dp[i][j-1]);


	if(ar[i]<j){dp[i][j]-=dp[i-1][j-1-ar[i]];}
}
//cout<<i<<" "<<j<<" "<<dp[i][j]<<endl;

dp[i][j]=(1000000007+dp[i][j])%1000000007;

}
cout<<dp[n-1][k];



}
