#include <iostream>
#include <vector>
#include <map>

using namespace std;

int main(){

int n, k;

cin>> n >> k;


vector <long long> a(n), sa(n+1);

sa[0] = 0;

map<long long, int> amap;
amap[0] = 1;
long long ans = 0;

for(int i=0; i<n; i++){
int tmp;
cin >> tmp;
a[i] = tmp - 1;
sa[i+1] = (sa[i] + a[i]) % k;
ans += amap[sa[i+1]];
amap[sa[i+1]] += 1;
if(i-k+2>=0) amap[sa[i-k+2]]--;
}
  
  
if(k==1) ans = 0;

cout << ans << endl;
}

### Prompt

Please create a solution in cpp 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 <iostream>
#include <vector>
#include <map>

using namespace std;

int main(){

int n, k;

cin>> n >> k;


vector <long long> a(n), sa(n+1);

sa[0] = 0;

map<long long, int> amap;
amap[0] = 1;
long long ans = 0;

for(int i=0; i<n; i++){
int tmp;
cin >> tmp;
a[i] = tmp - 1;
sa[i+1] = (sa[i] + a[i]) % k;
ans += amap[sa[i+1]];
amap[sa[i+1]] += 1;
if(i-k+2>=0) amap[sa[i-k+2]]--;
}
  
  
if(k==1) ans = 0;

cout << ans << endl;
}

```