#include <bits/stdc++.h>
using namespace std;
#define rep(i,m,n) for(int i=m;i<n;i++)
typedef pair<int,int> P;
typedef long long ll;

int main() {
  int n;
  ll k;
  cin>>n>>k;
  ll a[n];
  rep(i,0,n) cin>>a[i];
  ll s[n+1];
  s[0]=0;
  rep(i,0,n) s[i+1]=s[i]+a[i];
  ll t[n];
  rep(i,0,n+1) s[i]=(s[i]-i)%k;
  map<ll,ll> b;
  ll ans=0;
  rep(i,0,n+1){
    ans+=b[s[i]];
    b[s[i]]++;
    if(i+1-k>=0) b[s[i+1-k]]--;
  }
  cout<<ans<<endl;
}

### Prompt

In CPP, your task is to solve 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;
#define rep(i,m,n) for(int i=m;i<n;i++)
typedef pair<int,int> P;
typedef long long ll;

int main() {
  int n;
  ll k;
  cin>>n>>k;
  ll a[n];
  rep(i,0,n) cin>>a[i];
  ll s[n+1];
  s[0]=0;
  rep(i,0,n) s[i+1]=s[i]+a[i];
  ll t[n];
  rep(i,0,n+1) s[i]=(s[i]-i)%k;
  map<ll,ll> b;
  ll ans=0;
  rep(i,0,n+1){
    ans+=b[s[i]];
    b[s[i]]++;
    if(i+1-k>=0) b[s[i+1-k]]--;
  }
  cout<<ans<<endl;
}

```