#include <iostream>
#include <vector>
#include <map>
using namespace std;

typedef long long ll;

ll ans;
ll sum[200005];
map<ll,int> num;

int main() {
  ll n,k;
  cin >> n >> k;
  for(int i = 0; i < n; i++) {
    ll a;
    cin >> a;
    a--;
    sum[i+1] = (sum[i] + a) % k;
  }

  num[0]++;
  
  for(int i = 1; i <= n; i++) {
    if(i - k >= 0) num[sum[i-k]]--;
    ans += num[sum[i]]++;
   
  }

  cout << ans << endl;
}
  
    
  

### Prompt

Create a solution in Cpp for 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 <iostream>
#include <vector>
#include <map>
using namespace std;

typedef long long ll;

ll ans;
ll sum[200005];
map<ll,int> num;

int main() {
  ll n,k;
  cin >> n >> k;
  for(int i = 0; i < n; i++) {
    ll a;
    cin >> a;
    a--;
    sum[i+1] = (sum[i] + a) % k;
  }

  num[0]++;
  
  for(int i = 1; i <= n; i++) {
    if(i - k >= 0) num[sum[i-k]]--;
    ans += num[sum[i]]++;
   
  }

  cout << ans << endl;
}
  
    
  

```