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

int main() {
    int N, K; cin >> N >> K;
    vector<int> A(N);
    for(auto &e : A) cin >> e;
    vector<int64_t> S(N + 1);
    for(int i = 0; i < N; ++i) S[i + 1] = S[i] + A[i];
    for(int i = 1; i <= N; ++i) S[i] = (S[i] - i) % K;
    map<int, int> ma;
    int64_t ans = 0;
    for(int i = 0; i <= N; ++i) {
        ans += ma[S[i]];
        ma[S[i]]++;
        if(i - K + 1 >= 0) ma[S[i - K + 1]]--;
    }
    cout << ans << '\n';
    return 0;
}

### Prompt

Your task is to create 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;

int main() {
    int N, K; cin >> N >> K;
    vector<int> A(N);
    for(auto &e : A) cin >> e;
    vector<int64_t> S(N + 1);
    for(int i = 0; i < N; ++i) S[i + 1] = S[i] + A[i];
    for(int i = 1; i <= N; ++i) S[i] = (S[i] - i) % K;
    map<int, int> ma;
    int64_t ans = 0;
    for(int i = 0; i <= N; ++i) {
        ans += ma[S[i]];
        ma[S[i]]++;
        if(i - K + 1 >= 0) ma[S[i - K + 1]]--;
    }
    cout << ans << '\n';
    return 0;
}

```