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 File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            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());
        }
    }
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		Integer[] a = new Integer[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		
		Arrays.sort(a);		
		
		
				
		
		int[] counts = new int[200005];
		int[] totalMoves = new int[200005];
		
		for (int val : a) {
			int moves = 0;
			
			while (val > 0) {
				if (counts[val] < k) {
					counts[val]++;
					totalMoves[val] += moves;
				}
				
				moves++;
				val /= 2;
			}
		}
		
		
		int res = Integer.MAX_VALUE;
		for (int i = 0; i <= 200000; i++) {
			if (counts[i] == k) {
				res = Math.min(res, totalMoves[i]);
			}
		}
		
		
		
		out.println(res);
		
		
		
		
		
		
		
		
		out.close();
	}
}