#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
int main(){
    long long n,k;
    cin >> n >> k;
    long long a[n];
    rep(i,n) cin >> a[i];
    rep(i,n) a[i]--;
    long long suma[n+1];
    suma[0] = 0;
    rep(i,n) suma[i+1]=(suma[i]+a[i])%k;
    map<long long,int> mp;
    rep(i,min(n+1,k)) mp[suma[i]]++;
    long long ans = 0;
    rep(i,n){
        mp[suma[i]]--;
        ans+=mp[suma[i]];
        if((k+i)<=n)mp[suma[i+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,n) for(int i=0;i<n;i++)
int main(){
    long long n,k;
    cin >> n >> k;
    long long a[n];
    rep(i,n) cin >> a[i];
    rep(i,n) a[i]--;
    long long suma[n+1];
    suma[0] = 0;
    rep(i,n) suma[i+1]=(suma[i]+a[i])%k;
    map<long long,int> mp;
    rep(i,min(n+1,k)) mp[suma[i]]++;
    long long ans = 0;
    rep(i,n){
        mp[suma[i]]--;
        ans+=mp[suma[i]];
        if((k+i)<=n)mp[suma[i+k]]++;
    }
    cout << ans << endl;
}
```