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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Solver {

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

    static Scanner in = new Scanner(System.in);
    static PrintWriter out;
    static int n;
    static int k;
    static int a[];

    void read() throws IOException {
        out = new PrintWriter(System.out);
        int test = 1;
        while (test-- > 0) {
            n = in.nextInt();
            k = in.nextInt();
            a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            solve();
        }
    }


    void solve() throws IOException {
        ArrayList<Integer> val[] = new ArrayList[2 * 100000 + 1];
        for (int i = 0; i < 2 * 100000 + 1; i++) {
            val[i] = new ArrayList<>();
        }
        for (int i = 0; i < n; i++) {
            int op = 0;
            while (a[i] > 0) {
                val[a[i]].add(op++);
                a[i] >>= 1;
            }
        }
        int ans = (int) 1e9;
        for (int i = 0; i < 2 * 100000 + 1; i++) {
            if (val[i].size() >= k) {
                Collections.sort(val[i]);
                int cur = 0;
                for (int j = 0; j < k; j++) {
                    cur += val[i].get(j);
                }
                ans = Math.min(ans, cur);
            }
        }
        System.out.println(ans);
    }
}

class FastScanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

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

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

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