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

int main(){
    int N, K;
    cin >> N >> K;
    vector<int64_t> A(N), S(N+1);
    for(int i=0; i<N; i++){
        cin >> A[i];
        A[i]--;
        S[i+1] = (S[i] + A[i] + K) % K;
    }

    map<int, int> mp;
    int64_t ans = 0;
    for(int i=0; i<=N; i++){
        if(i-K>=0) mp[S[i-K]]--;
        ans += mp[S[i]];
        mp[S[i]]++;
        
    }
    cout << ans << endl;
    return 0;
}

### Prompt

Please create a solution in Cpp 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;

int main(){
    int N, K;
    cin >> N >> K;
    vector<int64_t> A(N), S(N+1);
    for(int i=0; i<N; i++){
        cin >> A[i];
        A[i]--;
        S[i+1] = (S[i] + A[i] + K) % K;
    }

    map<int, int> mp;
    int64_t ans = 0;
    for(int i=0; i<=N; i++){
        if(i-K>=0) mp[S[i-K]]--;
        ans += mp[S[i]];
        mp[S[i]]++;
        
    }
    cout << ans << endl;
    return 0;
}

```