#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const int INF=1e9;
const ll LINF=1e18;

int main(){
    ll n,k;
    cin>>n>>k;
    ll a[n+1];
    a[0]=0;
    for(int i=0;i<n;i++){
        cin>>a[i+1];
        a[i+1]-=1;
        a[i+1]+=a[i];
        a[i+1]%=k;
    }
    ll ans=0;
    map<ll,int> mp;
    for(int i=0;i<=n;i++){
        if(i>=k)mp[a[i-k]]--;
        ans+=mp[a[i]];
        mp[a[i]]++;
    }
    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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const int INF=1e9;
const ll LINF=1e18;

int main(){
    ll n,k;
    cin>>n>>k;
    ll a[n+1];
    a[0]=0;
    for(int i=0;i<n;i++){
        cin>>a[i+1];
        a[i+1]-=1;
        a[i+1]+=a[i];
        a[i+1]%=k;
    }
    ll ans=0;
    map<ll,int> mp;
    for(int i=0;i<=n;i++){
        if(i>=k)mp[a[i-k]]--;
        ans+=mp[a[i]];
        mp[a[i]]++;
    }
    cout<<ans<<endl;
}
```