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.*;
public class EqualElements{

     public static void main(String []args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int k = scan.nextInt();
        int [] numbers = new int[n];
        scan.nextLine();
        for(int i = 0; i < n; i++) {
            numbers[i] = scan.nextInt();
        }
        scan.close();
        System.out.println(minOperations(numbers, k));
     }
     
     public static int minOperations(int[] numbers, int k) {
        HashMap<Integer, ArrayList<Integer>> list = new HashMap<Integer, ArrayList<Integer>>();
        for(int i : numbers) {
            int counter = 0;
            while(i > 0) {
                if(!list.containsKey(i)) {
                    ArrayList<Integer> newList = new ArrayList<Integer>();
                    newList.add(counter);
                    list.put(i, newList);
                } else {
                    ArrayList<Integer> currList = list.get(i);
                    currList.add(counter);
                }
                counter++;
                i /= 2;
            }
        }
        
        int minValue = Integer.MAX_VALUE;
        for(int key : list.keySet()) {
            if(list.get(key).size() >= k) {
                ArrayList<Integer> currValueList = list.get(key);
                Collections.sort(currValueList);
                int sum = 0;
                for(int i = 0; i < k; i++) {
                    sum += currValueList.get(i);
                }
                minValue = Math.min(minValue, sum);
            }
        }
        return minValue;
    }
}