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:

//package codechef;
import java.io.*;
import java.util.*;


// Warning: Printing unwanted or ill-formatted data to output will cause the test cases to fail

public class GFG {
    public static void main(String args[] ) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String [] nm=reader.readLine().trim().split("\\s+");
        int n=Integer.parseInt(nm[0]);
        int m=Integer.parseInt(nm[1]);
        String[] inp=reader.readLine().trim().split("\\s+");
        ArrayList<Integer>[] count=new ArrayList[2*100000+11];
        for(int i=0;i<count.length;i++) {
        	count[i]=new ArrayList<Integer>();
        	//System.out.println(count[i].size());
        }
        for(int i=1;i<=n;i++) {
        	int k=Integer.parseInt(inp[i-1]);
        	int cur=0;
        	//System.out.print(count.get(k));
        	//count.get(k).add(cur);
        	count[k].add(cur);
        	while(k>0){
        		k/=2;
        		cur++;
        		count[k].add(cur);
        		//System.out.print(count[k].size()+" ");
        	}
        }
        int ans=Integer.MAX_VALUE;
        for(int i=0;i<count.length;i++) {
        	ArrayList<Integer> aa=count[i];
        	if(aa.size()<m) {
        		continue;
        	}
        	
        		Collections.sort(aa);
        		int sum=0;
        		for(int j=0;j<m;j++) {
        			sum+=(aa.get(j));
        		}
        		ans=Math.min(sum, ans);
        		//System.out.print(sum+" "+i+" ");
        	
        }
        System.out.println(ans);
    }
}