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.lang.*;
import java.util.*;
import java.io.*;

public class Main {
    void solve() {
        int n=ni(),K=ni();
        int M=200000;

        int a[]=new int[n+1];
        long ans=Long.MAX_VALUE;
        PriorityQueue<Integer> q[]=new PriorityQueue[M+1];
        for(int i=0;i<=M;i++)q[i]=new PriorityQueue<>();
        for(int i=1;i<=n;i++){
            a[i]=ni();
            int cc=0;
            q[a[i]].offer(0);
            while(a[i]>0){
                cc++;
                a[i]/=2;
                q[a[i]].offer(cc);
            }

        }
        int cnt,sm;
        for(int i=0;i<=M;i++){
            if(q[i].size()<K) continue;
            cnt=K; sm=0;

            while(!q[i].isEmpty() && cnt>0){
                sm+=q[i].poll();
                cnt--;
            }
            ans=Math.min(ans,sm);

        }
        pw.println(ans);



    }
    class Node implements Comparable<Node>{
        int num;
        int cnt;
        public Node(int num,int cnt){
            this.num=num;
            this.cnt=cnt;
        }
        public int compareTo(Node c){
            int t=Integer.compare(this.num,c.num);
            if(t!=0) return t;
            return Integer.compare(this.cnt,c.cnt);
        }
    }

    long M = (long)1e9+7;
    // END
    PrintWriter pw;
    StringTokenizer st;
    BufferedReader br;

    void run() throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
    }
    public static void main(String[] args) throws Exception {
        new Main().run();
    }

    String ns() {
        while (st == null || !st.hasMoreElements()) {

            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    String nextLine() throws Exception {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            throw new Exception(e.toString());
        }
        return str;
    }

    int ni() {
        return Integer.parseInt(ns());
    }

    long nl() {
        return Long.parseLong(ns());
    }

    double nd() {
        return Double.parseDouble(ns());
    }
}