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.*;
import java.math.*;
public class Main{
        private static int max=200*1000+5;
        public static void main(String args[]){
                Scanner sc=new Scanner(System.in);
                int n=sc.nextInt();
                int k=sc.nextInt();
                int a[]=new int[n];
                for(int i=0;i<n;i++){
                        a[i]=sc.nextInt();
                }
                List<Integer> [] vals=new ArrayList[max];
                for(int i=0;i<max;i++){
                        vals[i]=new ArrayList<Integer>();
                }
                for(int i:a){
                        int y=i;
                        int cur=0;
                        while(y>0){
                                
                                vals[y].add(cur);
                                y=y/2;
                                cur++;
                        }
                }
                int res=Integer.MAX_VALUE;
                for(List<Integer> l:vals){
                        if(l.size()>=k){
                                Collections.sort(l);
                                int t=0;
                                for(int i=0;i<k;i++){
                                        t+=l.get(i);
                                }
                                 res=Math.min(t,res);
                        }
                       
                }
                System.out.println(res);
        }
}