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

int main() {
    int N; cin >> N;
    long long K; cin >> K;

    vector<long long> S(N + 1, 0);
    for(int i=0; i<N; ++i) {
        cin >> S[i + 1];
        S[i + 1] += S[i];
    }

    long long res = 0;
    map<long long, int> cnt;
    cnt[0] = 1;
    for(int i=1; i<=N; ++i) {
        if(i >= K) cnt[(S[i - K] - (i - K)) % K] -= 1;
        res += cnt[(S[i] - i) % K];
        cnt[(S[i] - i) % K] += 1;
    }
    cout << res << endl;
}
### Prompt

Please formulate 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; cin >> N;
    long long K; cin >> K;

    vector<long long> S(N + 1, 0);
    for(int i=0; i<N; ++i) {
        cin >> S[i + 1];
        S[i + 1] += S[i];
    }

    long long res = 0;
    map<long long, int> cnt;
    cnt[0] = 1;
    for(int i=1; i<=N; ++i) {
        if(i >= K) cnt[(S[i - K] - (i - K)) % K] -= 1;
        res += cnt[(S[i] - i) % K];
        cnt[(S[i] - i) % K] += 1;
    }
    cout << res << endl;
}
```