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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

import static java.lang.Math.min;

public class D2_1312 {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] __) {
        FastReader sc = new FastReader();
        int n = sc.nextInt(), k = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) arr[i] = sc.nextInt();
        Map<Integer, List<Integer>> map = new HashMap<>();
        for (int x : arr) {
            int cnt = 0;
            while (x > 0) {
                if (map.containsKey(x)) map.get(x).add(cnt);
                else {
                    List<Integer> al = new ArrayList<>();
                    al.add(cnt);
                    map.put(x, al);
                }
                cnt++;
                x /= 2;
            }
        }
        int ans = Integer.MAX_VALUE;
        for (int x : map.keySet()) {
            List<Integer> cur = map.get(x);
            if (cur.size() >= k) {
                Collections.sort(cur);
                int su = 0;
                for (int i = 0; i < k; i++) su += cur.get(i);
                ans = min(ans, su);
            }
        }
        System.out.println(ans);
    }
}