#include<bits/stdc++.h>
using namespace std;
using ll = long long;
int main(){
    int n,k;cin>>n>>k;
    vector<int> arr(n);
   for(int i = 0; i < n; i++) cin>>arr[i];
   for(int i = 0; i < n; i++) arr[i]--;
   vector<ll> s(n+1);
   for(int i = 0; i < n;  i++) s[i+1] = (s[i]+arr[i])%k;
   map<ll,ll> mp;
   ll ans = 0;
   queue<ll> q;
   for(int i = 0; i <= n; i++){
       ans+=mp[s[i]];
       mp[s[i]]++;
       q.push(s[i]);
       if(q.size() == k){
           mp[q.front()]--;
           q.pop();
       }
   }
  cout<<ans;
}

### Prompt

Generate a Cpp solution to the following problem:

Given are a sequence of N positive integers A_1, A_2, \ldots, A_N, and a positive integer K.

Find the number of non-empty contiguous subsequences in A such that the remainder when dividing the sum of its elements by K is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.

Constraints

* All values in input are integers.
* 1 \leq N \leq 2\times 10^5
* 1 \leq K \leq 10^9
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \cdots A_N


Output

Print the number of subsequences that satisfy the condition.

Examples

Input

5 4
1 4 2 3 5


Output

4


Input

8 4
4 2 4 2 4 2 4 2


Output

7


Input

10 7
14 15 92 65 35 89 79 32 38 46


Output

8

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
int main(){
    int n,k;cin>>n>>k;
    vector<int> arr(n);
   for(int i = 0; i < n; i++) cin>>arr[i];
   for(int i = 0; i < n; i++) arr[i]--;
   vector<ll> s(n+1);
   for(int i = 0; i < n;  i++) s[i+1] = (s[i]+arr[i])%k;
   map<ll,ll> mp;
   ll ans = 0;
   queue<ll> q;
   for(int i = 0; i <= n; i++){
       ans+=mp[s[i]];
       mp[s[i]]++;
       q.push(s[i]);
       if(q.size() == k){
           mp[q.front()]--;
           q.pop();
       }
   }
  cout<<ans;
}

```