#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main(){
  ll n, k;
  cin >> n >> k;
  vector<ll> ai(n);
  vector<ll> tot(n+1);
  for(int i=0; i<n; ++i){
    cin >> ai.at(i);
    --ai.at(i);
    tot.at(i+1) = (tot.at(i) +ai.at(i))%k;
  }
  
  ll ans=0;
  map<ll,ll> mp;
  for(int i=0; i<n+1; ++i){
    ++mp[tot.at(i)];
    if(i-k>=0) --mp[tot.at(i-k)];
    ans += mp[tot.at(i)]-1;
  }
  cout << ans << endl;
}
### Prompt

Your challenge is to write 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;
typedef long long ll;

int main(){
  ll n, k;
  cin >> n >> k;
  vector<ll> ai(n);
  vector<ll> tot(n+1);
  for(int i=0; i<n; ++i){
    cin >> ai.at(i);
    --ai.at(i);
    tot.at(i+1) = (tot.at(i) +ai.at(i))%k;
  }
  
  ll ans=0;
  map<ll,ll> mp;
  for(int i=0; i<n+1; ++i){
    ++mp[tot.at(i)];
    if(i-k>=0) --mp[tot.at(i-k)];
    ans += mp[tot.at(i)]-1;
  }
  cout << ans << endl;
}
```