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
ll mod=(ll)1e9+7;

int main(){
  ios::sync_with_stdio(0);
  cin.tie(NULL); cout.tie(NULL); 
  ll n,k,i,j,a;
  cin>>n>>k;
  vector<ll> dp(k+1);
  dp[0]=1;
  
  for(j=0;j<n;j++){
    cin>>a;
    vector<ll> sub(k+1);
    swap(sub,dp);
    for(i=1;i<=k;i++)(sub[i]+=sub[i-1])%=mod;  
    for(i=0;i<=k;i++){
      ll left=i-a-1;
      dp[i]=sub[i];
      if(left>=0)dp[i]-=sub[left];
      (dp[i]+=mod)%=mod;
    }
    
  }
  cout<<dp[k];
}