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.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class CF1213C {

    static int cost(int [] a, int num, int k) {
//        System.out.println(num + " " + k);
        PriorityQueue<Integer> pq = new PriorityQueue<>();
        for (int i = 0; i < a.length; ++i) {
//            System.out.println(num + " " + pq);
           int cur  = compute(a[i], num);
           if (cur != Integer.MAX_VALUE) pq.add(-1 * cur);
           if (pq.size() > k) pq.remove();
        }

        int answer = 0;
        if (pq.size() != k) return Integer.MAX_VALUE;
//        System.out.println(pq);
        while(!pq.isEmpty())
            answer -= pq.remove();
        return answer;
    }

    private static int compute(int x, int num) {
        if (num > x) return Integer.MAX_VALUE;
        if (num == x) return 0;
        int cost = 0;
        while(x > num) {
            x /= 2;
            cost++;
        }
        if (x == num) return cost;
        else return Integer.MAX_VALUE;
    }


    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();
        Arrays.sort(a);
        int max = a[N - 1];

        int answer = Integer.MAX_VALUE;
        for (int i = 1; i <= max; i++) {
//            System.out.println(i + " " + cost(a, i, K));
            answer = Math.min(answer, cost(a, i, K));
        }
        out.println(answer);

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



    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();
        }


    }
}