Problem: You are given the array a consisting of n elements and the integer k ≤ n.

You want to obtain at least k equal elements in the array a. In one move, you can make one of the following two operations:

  * Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of a is mn then you choose such index i that a_i = mn and set a_i := a_i + 1); 
  * take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of a is mx then you choose such index i that a_i = mx and set a_i := a_i - 1). 



Your task is to calculate the minimum number of moves required to obtain at least k equal elements in the array.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and the required number of equal elements.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the minimum number of moves required to obtain at least k equal elements in the array.

Examples

Input


6 5
1 2 2 4 2 3


Output


3


Input


7 5
3 3 2 1 1 1 3


Output


4

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> arr(200005);
  for (int i = 0; i < 200005; i++) {
    arr[i] = 0;
  }
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    arr[x]++;
  }
  int minop = 100000000;
  for (int i = 1; i <= 200000; i++) {
    int ops = 0;
    int total = arr[i];
    if (total >= k) {
      cout << 0 << "\n";
      return 0;
    }
    int power = 0;
    bool hit = false;
    bool flag = false;
    while (!flag) {
      power++;
      int start = pow(2, power);
      for (int j = i * start; j < i * start + start; j++) {
        if (j > 200000) {
          flag = true;
          break;
        }
        ops += power * arr[j];
        total += arr[j];
        if (total >= k) {
          int r = total - k;
          ops -= power * r;
          flag = true;
          hit = true;
          break;
        }
      }
      if (flag) break;
    }
    if (!hit) continue;
    minop = min(minop, ops);
  }
  cout << max(minop, 0) << "\n";
}