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.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class D1213 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int K = in.nextInt();
        Map<Integer,List<Integer>> map = new HashMap<>();
        for (int n=0; n<N; n++) {
            int a = in.nextInt();
            int step = 0;
            while (true) {
                List<Integer> list = map.get(a);
                if (list == null) {
                    list = new ArrayList<>();
                    map.put(a, list);
                }
                list.add(step);
                step++;
                if (a == 0) {
                    break;
                } else {
                    a /= 2;
                }
            }
        }
        int min = Integer.MAX_VALUE;
        for (List<Integer> list : map.values()) {
            if (list.size() >= K) {
                Collections.sort(list);
                int count = 0;
                for (int i=0; i<K; i++) {
                    count += list.get(i);
                }
                min = Math.min(min, count);
            }
        }
        System.out.println(min);
    }

}