#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1000000007;
vector<pair<int,int>> hen[100000];
int iro[100000]={};

signed main() {
int n,k;
cin>>n>>k;
int d[n],a;
for(int i=0;i<n;i++){
    cin>>a;
    d[i]=(a+k-1)%k;
}
if(k==1){
    cout<<0;
    return 0;
}
int m[n+1];
m[0]=0;
for(int i=1;i<=n;i++)m[i]=(m[i-1]+d[i-1])%k;
map<int,int> ans;
int ans2=0;
ans[0]++;
for(int i=1;i<=n;i++){
    ans2+=ans[m[i]];
    ans[m[i]]++;
    if(i-k+1>=0)ans[m[i-k+1]]--;
}


cout<<ans2;


return 0;
}

### 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;
#define int long long
const int MOD = 1000000007;
vector<pair<int,int>> hen[100000];
int iro[100000]={};

signed main() {
int n,k;
cin>>n>>k;
int d[n],a;
for(int i=0;i<n;i++){
    cin>>a;
    d[i]=(a+k-1)%k;
}
if(k==1){
    cout<<0;
    return 0;
}
int m[n+1];
m[0]=0;
for(int i=1;i<=n;i++)m[i]=(m[i-1]+d[i-1])%k;
map<int,int> ans;
int ans2=0;
ans[0]++;
for(int i=1;i<=n;i++){
    ans2+=ans[m[i]];
    ans[m[i]]++;
    if(i-k+1>=0)ans[m[i-k+1]]--;
}


cout<<ans2;


return 0;
}

```