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 equalizedivision {
	public void run() throws Exception {
		Scanner file = new Scanner(System.in);
		int times = file.nextInt();
		int k = file.nextInt();
		ArrayList<Integer> w= new ArrayList();
		int max = Integer.MIN_VALUE;
		for (int i = 0; i < times; i++) {
			int temp = file.nextInt();
			w.add(temp);
			max = Math.max(max, temp);
		}
		Collections.sort(w);
		int[] kamt = new int[max + 1], moves = new int[max + 1];
		int min = Integer.MAX_VALUE;
		for (int i = 0; i < times; i++) {
			int temp = w.get(i);
			int count = 1;
			while (temp > 0) {
				kamt[temp]++;
				if (kamt[temp] >= k) min = Math.min(min, moves[temp]);
				temp /= 2;
				moves[temp] += count;
				count++;
			}
		}
		System.out.println(min);
	}

	public static void main(String[] args) throws Exception {
		new equalizedivision().run();
	}

}