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.*;
/*


 */









public class C {
    static FastReader sc=null;
    static int nax=(int)2e5+ 5;
    
    public static void main(String[] args) {
		sc=new FastReader();
		int n=sc.nextInt(),k=sc.nextInt();
		int a[]=sc.readArray(n);
		ruffleSort(a);
		int q=Integer.MAX_VALUE;
		for(int i=0;i<nax;i++) {
			int ans=0,val=i;			
			int b[]=new int[n];
			for(int j=0;j<n;j++)b[j]=a[j];
			int l=0;
			int curr=k;
			while(l<n && b[l]<val)l++;
			while(curr>0 && l<n) {
				int c=0;
				while(b[l]>val) {
					b[l]/=2;
					c++;
				}
				if(b[l]==val) {
					curr--;
					ans+=c;
				}
				l++;
			}
			//System.out.println(curr+" "+val+" "+ans);
			//print(b);
			if(curr==0)q=Math.min(q, ans);
		}
		System.out.println(q);

	
	}
    
   
  
    
    static void ruffleSort(int a[]) {
        ArrayList<Integer> al=new ArrayList<>();
        for(int i:a)al.add(i);
        Collections.sort(al);
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    static void ruffleSort(long a[]) {
        ArrayList<Long> al=new ArrayList<>();
        for(long i:a)al.add(i);
        Collections.sort(al);
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    
    static int[] reverse(int a[]) {
        ArrayList<Integer> al=new ArrayList<>();
        for(int i:a)al.add(i);
        Collections.sort(al,Collections.reverseOrder());
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
        return a;
    }
 
    static int gcd(int a,int b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
    static long gcd(long a,long b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
        
 
    
    
    
    static void print(long a[]) {
        for(long e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    static void print(char a[]) {
        for(char e:a) {
            System.out.print(e);
        }
        System.out.println();
    }
    
    
    static void print(int a[]) {
        for(int e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
        int[] readArray(int n) {
            int a[]=new int [n];
            for(int i=0;i<n;i++) {
                a[i]=sc.nextInt();
            }
            return a;
        }
    } 
}