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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

    static boolean canBeK(int i, int k) {
        while (i > k) {
            i = i >> 1;
        }
        return i == k;
    }

    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int n = scn.nextInt();
        int k = scn.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = scn.nextInt();
        scn.close();

        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int x = a[i];
            while (x > 0) {
                list.add(x);
                x = x >> 1;
            }
        }

        int ans = -1;
        for (int res : list) {
            ArrayList<Integer> cnt = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                int x = a[i];
                int cur = 0;
                while (x > res) {
                    x = x >> 1;
                    cur++;
                }
                if (x == res) cnt.add(cur);
            }
            if (cnt.size() >= k) {
                int sum = 0;
                cnt.sort(Integer::compareTo);
                for (int c = 0; c < k; c++) sum += cnt.get(c);
                if (ans == -1 || sum < ans) ans = sum;
            }
        }
        System.out.println(ans);
    }
}