#include <bits/stdc++.h>
long long int m,n,z,ans;
using namespace std;
long long int vp[200010],sum;
map<long long int,long long int>q;
int main()
{
    int n,k;
    scanf("%d %d",&n,&k);
    for(int i=1;i<=n;i++)
    {
        scanf("%lld",&vp[i]);
        vp[i]+=vp[i-1]-1;
    }
    for(int i=1;i<=n;i++)
        vp[i]%=k;
    q[0]++;
    for(int i=1;i<=n;i++)
    {
        if(i>=k)
            q[vp[i-k]]--;
sum+=q[vp[i]];
        q[vp[i]]++;

    }
    printf("%lld",sum);
}
### Prompt

Please formulate 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 <bits/stdc++.h>
long long int m,n,z,ans;
using namespace std;
long long int vp[200010],sum;
map<long long int,long long int>q;
int main()
{
    int n,k;
    scanf("%d %d",&n,&k);
    for(int i=1;i<=n;i++)
    {
        scanf("%lld",&vp[i]);
        vp[i]+=vp[i-1]-1;
    }
    for(int i=1;i<=n;i++)
        vp[i]%=k;
    q[0]++;
    for(int i=1;i<=n;i++)
    {
        if(i>=k)
            q[vp[i-k]]--;
sum+=q[vp[i]];
        q[vp[i]]++;

    }
    printf("%lld",sum);
}
```