#include<iostream>
#include<map>
#include<vector>
using namespace std;
typedef long long ll;

int main(){
    int n, k;
    cin >> n >> k;
    vector<ll> v(n+1, 0);
    for(int i = 1; i <= n; i++)  cin >> v[i], v[i] += v[i-1];
    map<ll,int> m;
    ll ret = 0;
    for(int i = 0; i <= n; i++){
        if(i >= k)   m[(v[i-k]-(i-k))%k]--;
        ret += m[(v[i]-i)%k];  
        m[(v[i]-i)%k]++;
    }
    cout << ret << endl;
    return 0;
}
### Prompt

Your task is to create a CPP solution 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<map>
#include<vector>
using namespace std;
typedef long long ll;

int main(){
    int n, k;
    cin >> n >> k;
    vector<ll> v(n+1, 0);
    for(int i = 1; i <= n; i++)  cin >> v[i], v[i] += v[i-1];
    map<ll,int> m;
    ll ret = 0;
    for(int i = 0; i <= n; i++){
        if(i >= k)   m[(v[i-k]-(i-k))%k]--;
        ret += m[(v[i]-i)%k];  
        m[(v[i]-i)%k]++;
    }
    cout << ret << endl;
    return 0;
}
```