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.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.StringTokenizer;

public class CF1213C {

    static final int MAXN = (int) (2e5 + 1);

    static boolean hasKEqualNumbers(int[] a, int N, int K) {
        HashMap<Integer, Integer> occ = new HashMap<>();
        for (int i = 0; i < N; ++i) {
            Integer curOcc = occ.getOrDefault(a[i], 0);
            if (curOcc + 1 >= K) return true;
            occ.put(a[i], curOcc + 1);
        }
        return false;
    }

    static ArrayList<Integer>[] powerOfTwoMap(int[] a, int N) {
        ArrayList<Integer>[] map = new ArrayList[MAXN];
        for (int i = 0; i < MAXN; ++i)
            map[i] = new ArrayList<>();

        for (int i = 0; i < N; ++i) {
            int cur = a[i];
            int divisions = 0;
            while (cur > 0) {
                map[cur].add(divisions);
                cur /= 2;
                divisions++;
            }
        }
        return map;
    }


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int N = sc.nextInt(), K = sc.nextInt();
        int[] a = new int[N];
        for (int i = 0; i < N; ++i) a[i] = sc.nextInt();

        if (hasKEqualNumbers(a, N, K)) {
            System.out.println(0);
            return;
        }

        ArrayList<Integer>[] map = powerOfTwoMap(a, N);
        int answer = Integer.MAX_VALUE;
        for (int i = 0; i < MAXN; ++i) {
            if (map[i].size() >= K) {
                Collections.sort(map[i]);
                answer = Math.min(answer, getSum(map[i], K));
            }
        }

        out.println(answer);

        out.flush();
        out.close();
    }

    private static int getSum(ArrayList<Integer> integers, int K) {
        int answer = 0;
        for (int i = 0; i < K; ++i) answer += integers.get(i);
        return answer;
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }


    }
}