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.io.*;
public class equalize{
	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; 
        } 
    } 
	public static void main(String args[]){
		FastReader sc=new FastReader();
		int n=sc.nextInt();
		int k=sc.nextInt();
		int a[]=new int[n];
		int max=0;
		ArrayList<ArrayList<Integer>> list=new ArrayList<>();
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
			if(a[i]>max){
				max=a[i];
			}
		}
		for(int i=0;i<=max;i++){
			list.add(i,new ArrayList<Integer>());
		}
		for(int i=0;i<n;i++){
			int op=0;
			while(true){
				list.get(a[i]).add(op);
				if(a[i]==0)
					break;
				a[i]/=2;
				op++;
			}
		}
		int s=list.size();
		int res=Integer.MAX_VALUE;
		for(int i=0;i<s;i++){
			int sum=0;
			if(list.get(i).size()>=k){
				Collections.sort(list.get(i));
				for(int j=0;j<k;j++){
					sum+=list.get(i).get(j);
				}
				if(sum<res)
					res=sum;
			}
		}
		System.out.println(res);
	}
}