#include <iostream>
#include <map>
using namespace std;
typedef long long ll;

int main()
{
    int n;
    ll k;
    cin >> n >> k;
    ll a[200005];
    for(int i = 0; i < n; i++){
        cin >> a[i];
        a[i]--;
    }
    ll s[200005];
    s[0] = 0;
    for(int i = 1; i <= n; i++) s[i] = (s[i - 1] + a[i - 1]) % k;
    map<ll, ll> mp;
    ll ans = 0;
    for(int i = 0; i <= n; i++){
        if(i >= k) mp[s[i - k]]--;
        ans += mp[s[i]];
        mp[s[i]]++;
    }
    cout << ans << endl;
}

### Prompt

Your challenge is to write 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 <iostream>
#include <map>
using namespace std;
typedef long long ll;

int main()
{
    int n;
    ll k;
    cin >> n >> k;
    ll a[200005];
    for(int i = 0; i < n; i++){
        cin >> a[i];
        a[i]--;
    }
    ll s[200005];
    s[0] = 0;
    for(int i = 1; i <= n; i++) s[i] = (s[i - 1] + a[i - 1]) % k;
    map<ll, ll> mp;
    ll ans = 0;
    for(int i = 0; i <= n; i++){
        if(i >= k) mp[s[i - k]]--;
        ans += mp[s[i]];
        mp[s[i]]++;
    }
    cout << ans << endl;
}

```