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.io.*;
import java.lang.*;
import java.util.*;

public class D2_1213 {
    public static void main(String[] args) throws IOException{
        int ans = Integer.MAX_VALUE;
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        HashMap<Integer, Integer> hash = new HashMap<>();
        HashMap<Integer, Integer> hash1 = new HashMap<>();
        st = new StringTokenizer(f.readLine());
        Integer[] arr = new Integer[n];
        for(int i = 0; i < n; i++){
            arr[i] = Integer.parseInt(st.nextToken());
        }
        Arrays.sort(arr);
        for(int i = 0; i < n; i++){
            int curr = arr[i];
            int divides = 0;
            while(curr != 0){
                if(!hash.containsKey(curr)){
                    hash.put(curr, 0);
                    hash1.put(curr, 0);
                }
                hash.put(curr, hash.get(curr)+1);
                hash1.put(curr, hash1.get(curr)+divides);
                if(hash.get(curr) >= k){
                    ans = Math.min(hash1.get(curr), ans);
                }
                curr/=2;
                divides++;
            }
            if(!hash.containsKey(0)){
                hash.put(curr, 0);
                hash1.put(curr, 0);
            }
            hash.put(curr, hash.get(curr)+1);
            hash1.put(curr, hash1.get(curr)+divides);
        }
        f.close();
        //System.out.println(hash);


        System.out.println(ans);
    }

}