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.*;
 
public class Main {
	static class pair{
		int cost;int occ;
		pair(int x,int y){
			cost=x;occ=y;
		}
	}
	public static void main(String[] args) throws IOException {
		MScanner sc=new MScanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();int k=sc.nextInt();
		PriorityQueue<Integer>nums[]=new PriorityQueue[(int)2e5+1];for(int i=0;i<nums.length;i++)nums[i]=new PriorityQueue<Integer>();
		long ans=1000000000;
		for(int i=0;i<n;i++) {
			int cost=0;int x=sc.nextInt();
			while(x>0) {
				nums[x].add(cost);
				cost++;
				x/=2;
			}
		}
		for(int i=0;i<nums.length;i++) {
			long cost=0;
			int o=0;
			while(o<k && !nums[i].isEmpty()) {
				cost+=nums[i].poll();o++;
			}
			if(o==k) {
				ans=Math.min(ans, cost);
			}
		}
		pw.println(ans);
		pw.flush();
	}
    static class MScanner {
		StringTokenizer st;
		BufferedReader br;
 
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}