#include <iostream>
#include <map>
using namespace std;
int n,k,a[200001];
map<int,int> mp;
int main(){
    cin>>n>>k;
    long long ans=0;
    mp[0]=1;
    for(int i=1;i<=n;i++){
        cin>>a[i];
        a[i]--;
        (a[i]+=a[i-1])%=k;
        if(i>=k)mp[a[i-k]%k]--;
        ans+=mp[a[i]%k];
        mp[a[i]%k]++;
    }
    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 <map>
using namespace std;
int n,k,a[200001];
map<int,int> mp;
int main(){
    cin>>n>>k;
    long long ans=0;
    mp[0]=1;
    for(int i=1;i<=n;i++){
        cin>>a[i];
        a[i]--;
        (a[i]+=a[i-1])%=k;
        if(i>=k)mp[a[i-k]%k]--;
        ans+=mp[a[i]%k];
        mp[a[i]%k]++;
    }
    cout<<ans<<endl;
}
```