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.util.*;
import java.io.*;

public class D {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int[] arr = new int[n];
        for(int i = 0; i  < n; i++) arr[i] = scanner.nextInt();
        int max = 200001;
        PriorityQueue<Integer>[] qs = new PriorityQueue[max];
        for(int i = 0; i < max; i++) {
            qs[i] = new PriorityQueue<>();
        }
        for(int i = 0; i < n; i++) {
            int cnt = 0;
            while(arr[i] > 0) {
                qs[arr[i]].add(cnt);
                cnt++;
                arr[i]/=2;
            }
            qs[arr[i]].add(cnt);
        }
        int best = Integer.MAX_VALUE;
        for(int i = 0; i < max; i++) {
            if (qs[i].size() >= k) {
                int sum = 0;
                for(int j = 0; j < k; j++) {
                    sum += qs[i].poll();
                }
                best = Math.min(sum, best);
            }
        }
        out.println(best);
        out.flush();
    }
    
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}