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 D2{
    public static void main(String args[]) throws IOException{
        Reader.init();
        int n=Reader.nextInt();
        int k=Reader.nextInt();
        int A[]=new int[n];
        for(int i=0;i<n;i++){
            A[i]=Reader.nextInt();
        }
        
        ArrayList<Integer> list[]=new ArrayList[200001];
        for(int i=0;i<200001;i++){
            list[i]=new ArrayList<Integer>();
        }
        
        for(int i=0;i<n;i++){
            int num=A[i];
            int cost=0;
            
            while(num>0){
                list[num].add(cost);
                num=num/2;
                cost++;
            }
        }
        
        int minCost=Integer.MAX_VALUE;
        for(int i=0;i<200001;i++){    	
            if(list[i].size()>=k){
            	Collections.sort(list[i]);
                int cost=0;
                for(int j=0;j<k;j++){
                    cost+=list[i].get(j);
                }
                
                minCost=Math.min(minCost, cost);
            }
        }
      
        System.out.println(minCost);
    }
}

class Node{
    int cost;
    int count;
    int num;
    Node(int c){
        cost=0;
        count=c;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init() {
        reader = new BufferedReader(new InputStreamReader(System.in) );
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            tokenizer = new StringTokenizer(reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }

    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    
}