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.util.Arrays;

public class competetive  {

     public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        String nki = br.readLine();
        String[]nk=nki.trim().split(" ");
        int n=Integer.parseInt(nk[0]);
        int k=Integer.parseInt(nk[1]);
        String line=br.readLine();
        String []s=line.trim().split(" ");
        int[]a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=Integer.parseInt(s[i]);
        }
        int []f=new int[200001];
        int []m=new int[200001];
        Arrays.sort(a);
        for(int i=0;i<n;i++){
            int c=0;
            int num=a[i];
            while(num>0){
                if(f[num]<k)
                    m[num]+=c;
                f[num]++;

                num/=2;
                c++;
            }
            f[0]++;
            m[0]+=c;
        }
        int min=Integer.MAX_VALUE;
        for(int i=0;i<f.length;i++){
            if(f[i]>=k){
                min=Math.min(min,m[i]);
            }
        }
        out.write(String.valueOf(min));

        out.flush();
    }
}