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

using ll = long long;
using Pi = pair < int , int >;

map < ll , ll > mp;
ll N, K;
ll ans = 0;
ll sum[200005] = {};
ll A[200005];

int main()
{
    mp[0] = 1;
    cin >> N >> K;
    for ( int i = 1; i <= N; i++ ) {
        cin >> A[i];
        sum[i] = (sum[i - 1] + A[i] - 1) % K;
        if ( i >= K ) mp[sum[i - K]]--;
        ans += mp[sum[i]]++;
    }

    cout << ans << endl;

    return ( 0 );
}

### Prompt

In Cpp, your task is to solve 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;

using ll = long long;
using Pi = pair < int , int >;

map < ll , ll > mp;
ll N, K;
ll ans = 0;
ll sum[200005] = {};
ll A[200005];

int main()
{
    mp[0] = 1;
    cin >> N >> K;
    for ( int i = 1; i <= N; i++ ) {
        cin >> A[i];
        sum[i] = (sum[i - 1] + A[i] - 1) % K;
        if ( i >= K ) mp[sum[i - K]]--;
        ans += mp[sum[i]]++;
    }

    cout << ans << endl;

    return ( 0 );
}

```