#include <bits/stdc++.h>
using namespace std;
#define REP(a,b) for(int a = 0;a < b;++a)
int main(){
   long long ans = 0;
long long n,k;
cin >> n>>k;
long long now = 0;
map<long long,long long> go;
go[0] = 1;
queue<long long> nya;
nya.push(0);
REP(i,n){
long long a;
cin >> a;
a--;now += a;now %= k;
nya.push(now);
while(nya.size() > k){
int now = nya.front();
nya.pop();
go[now]--;
}
ans += go[now];
go[now]++;
}
cout << ans << endl;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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;
#define REP(a,b) for(int a = 0;a < b;++a)
int main(){
   long long ans = 0;
long long n,k;
cin >> n>>k;
long long now = 0;
map<long long,long long> go;
go[0] = 1;
queue<long long> nya;
nya.push(0);
REP(i,n){
long long a;
cin >> a;
a--;now += a;now %= k;
nya.push(now);
while(nya.size() > k){
int now = nya.front();
nya.pop();
go[now]--;
}
ans += go[now];
go[now]++;
}
cout << ans << endl;
}
```