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

int main() {
    ll N, K; cin >> N >> K;
    vector<ll> A(N); for (int i = 0; i < N; i++) cin >> A[i];
    vector<ll> cum(N); cum[0] = (K + A[0] - 1) % K;
    for (int i = 1; i < N; i++) cum[i] = (K + A[i] + cum[i-1] - 1) % K;
    ll ans = 0;
    map<ll, ll> group;

    group[0]++;
    for (int i = 0; i < N; i++) {
        if (i == K-1) group[0]--;
        if (i >= K) group[cum[i-K]]--;
        ans += group[cum[i]]++;
    }
    cout << ans << endl;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
typedef long long ll;

int main() {
    ll N, K; cin >> N >> K;
    vector<ll> A(N); for (int i = 0; i < N; i++) cin >> A[i];
    vector<ll> cum(N); cum[0] = (K + A[0] - 1) % K;
    for (int i = 1; i < N; i++) cum[i] = (K + A[i] + cum[i-1] - 1) % K;
    ll ans = 0;
    map<ll, ll> group;

    group[0]++;
    for (int i = 0; i < N; i++) {
        if (i == K-1) group[0]--;
        if (i >= K) group[cum[i-K]]--;
        ans += group[cum[i]]++;
    }
    cout << ans << endl;
}

```