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.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;

public class Main {
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] str;
		str = br.readLine().split(" ");
		int n = Integer.parseInt(str[0]), k = Integer.parseInt(str[1]);
		str = br.readLine().split(" ");
		int[] arr = new int[n];
		for(int i=0; i<n; i++) arr[i] = Integer.parseInt(str[i]);
		List<Integer>[] values = new ArrayList[200009];
		for(int i=0; i<200009; i++) values[i] = new ArrayList<Integer>();
		for(int i=0; i<n; i++) {
			int x = arr[i];
			int cnt = 0;
			while(x>0) {
				values[x].add(cnt);
				cnt++;
				x = x>>1;
			}
		}
		int ans = Integer.MAX_VALUE;
		for(int i=0; i<200009; i++) {
			if(values[i].size()>=k) {
				Collections.sort(values[i]);
				int tmpAns = 0;
				for(int j=0; j<k; j++) tmpAns+=values[i].get(j);
				ans = Math.min(ans, tmpAns);
			}
		}
		System.out.println(ans);
	}
}