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.awt.*;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public Main() throws FileNotFoundException {
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    int b[][];

    TreeMap<Integer, Integer> count(int x) {
        TreeMap<Integer, Integer> tm = new TreeMap<>();
        int d = 0;
        while (x > 0) {
            tm.put(x, d);
            d++;
            x /= 2;
        }
        return tm;
    }

    void run() throws IOException {
        int n = nextInt();
        int k = nextInt();
        int[] a = new int[n];
        TreeMap<Integer, Integer> tm[] = new TreeMap[n];
        for (int i = 0; i < tm.length; i++) {
            tm[i] = new TreeMap<>();
        }
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
            tm[i] = count(a[i]);
        }
        long ans = Long.MAX_VALUE;
        for (int i = 0; i <= 2 * (int) 1e5; i++) {
            ArrayList<Integer> al = new ArrayList<>();
            for (int j = 0; j < n; j++) {
                if (tm[j].containsKey(i)) {
                    al.add(tm[j].get(i));
                }
            }
            if (al.size() < k) continue;
            Collections.sort(al);
            long sum = 0;
            for (int j = 0; j < k; j++) {
                sum += al.get(j);
            }
            ans = min(ans, sum);
        }
        pw.print(ans);
        pw.close();
    }

    class Pair {
        int x, y;

        public Pair(int a, int b) {
            x = a;
            y = b;
        }
    }
}