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.lang.reflect.Array;
import java.util.*;

/*CODE BY SHIKHAR TYAGI*/

public class D {
    public static void main(String args[]) {
        FastScanner scn = new FastScanner();
        int n = scn.nextInt();
        int k = scn.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = scn.nextInt();
        }
        PriorityQueue<Integer> q[] = new PriorityQueue[200001];
        for (int i = 0; i < n; ++i) {
            int cur = a[i];
            int count = 0;
            while (cur > 0) {
                if(q[cur] == null){
                    q[cur] = new PriorityQueue<>();
                }
                q[cur].add(count);
                cur /= 2;
                count++;
            }
        }

        int ans = Integer.MAX_VALUE;
        for (int i = 0; i <= 200000; ++i) {
            if (q[i]!= null && q[i].size() < k) {
                continue;
            }
            ans = Math.min(ans, getSum(q[i], k));
        }
        System.out.println(ans);
    }

    private static int getSum(PriorityQueue<Integer> integers, int k) {
        if(integers==null){
            return Integer.MAX_VALUE;
        }
        int sum = 0;
        int i = 0;
        while (i < k) {
            sum += integers.poll();
            i++;
        }
        return sum;
    }


    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

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

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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