#include <iostream>
#include <map>
using namespace std;

long s[200010];

int main()
{
    int n, K; cin>>n>>K;

    for(int a, i=0; i<n; ++i) {
        cin>>a;
        s[i+1]=s[i]+a;
    }

    map<int, int> mp;
    long res=0;
    for(int i=0; i<=n; ++i) {
        s[i]=(s[i]-i+K)%K;
        res+=mp[s[i]]++;
        if (i+1>=K) mp[s[i+1-K]]--;
    }
    cout<<res<<endl;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;

long s[200010];

int main()
{
    int n, K; cin>>n>>K;

    for(int a, i=0; i<n; ++i) {
        cin>>a;
        s[i+1]=s[i]+a;
    }

    map<int, int> mp;
    long res=0;
    for(int i=0; i<=n; ++i) {
        s[i]=(s[i]-i+K)%K;
        res+=mp[s[i]]++;
        if (i+1>=K) mp[s[i+1-K]]--;
    }
    cout<<res<<endl;
}

```