#include<bits/stdc++.h>
using namespace std;
long long arr[1000000];
long long brr[1000000];
int main(){
    int n,k;cin>>n>>k;
    for(int i=1;i<=n;i++){
        cin >>arr[i];
        brr[i] = arr[i] +brr[i-1];
    }
    for(int i=1;i<=n;i++){
        brr[i]=(brr[i] - i%k +k)%k;
    }
    map<long long ,int >mp;
    long long sum =0;
    for(int i=0;i<=n;i++){
        if(i>=k){
            mp[brr[i-k]]--;
        }
        sum+=mp[brr[i]];
        mp[brr[i]]++;
    }cout<<sum<<endl;
    return 0;

}


### 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;
long long arr[1000000];
long long brr[1000000];
int main(){
    int n,k;cin>>n>>k;
    for(int i=1;i<=n;i++){
        cin >>arr[i];
        brr[i] = arr[i] +brr[i-1];
    }
    for(int i=1;i<=n;i++){
        brr[i]=(brr[i] - i%k +k)%k;
    }
    map<long long ,int >mp;
    long long sum =0;
    for(int i=0;i<=n;i++){
        if(i>=k){
            mp[brr[i-k]]--;
        }
        sum+=mp[brr[i]];
        mp[brr[i]]++;
    }cout<<sum<<endl;
    return 0;

}


```