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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.Scanner;
import java.util.StringTokenizer;
 
public class temp {
	
	void solve() throws IOException {
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		int a[] = new int[n];
		
		for(int i=0;i<n;i++)
			a[i] = sc.nextInt();
		
		int N = (int)(2e5) + 1;
		ArrayList<Integer> x[] = new ArrayList[N];
		
		for(int i=0;i<N;i++)
			x[i] = new ArrayList<Integer>();
		
		for(int i=0;i<n;i++)
		{
			int d = a[i] , cost = 0;
			while(d!=0)
			{
				x[d].add(cost);
				cost++;
				d/=2;
			}
			x[0].add(cost);
		}
		
		int ans = Integer.MAX_VALUE;
		
		for(int i=0;i<N;i++)
		{
			if(x[i].size() >= k)
			{
				x[i].sort(null);
				int p = 0;
				for(int j=0;j<k;j++)
					p += x[i].get(j);
				
				ans = Math.min(ans , p);
			}
		}
		
		System.out.println(ans);
	}
 
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		new temp().solve();
	}
 
	class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			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());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}