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 F {
    public static class Number implements Comparable<Number>{
        int val;
        int cost;
        public Number(int v, int c){
            this.val = v;
            this.cost = c;
        }

        @Override
        public int compareTo(Number o) {
            if(this.val == o.val){
                return this.cost - o.cost;
            }
            else{
                return this.val - o.val;
            }
        }
    }
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(reader.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int[] array = new int[n];
        st = new StringTokenizer(reader.readLine());
        for(int i = 0; i < n; ++i){
            array[i] = Integer.parseInt(st.nextToken());
        }
        ArrayList<Number> arrayList = new ArrayList<>();
        for(int i = 0; i < n; ++i){
            int counter = 0;
            while(array[i] > 0){
                arrayList.add(new Number(array[i], counter));
                array[i] /= 2;
                ++counter;
            }
            arrayList.add(new Number(0, counter));
        }
        Collections.sort(arrayList);
        int ans = Integer.MAX_VALUE;
        int counter = 1;
        int cost = arrayList.get(0).cost;
        for(int i = 1; i < arrayList.size(); ++i){
            if(counter >= k){
                ans = Math.min(ans, cost);
            }
            if(arrayList.get(i).val != arrayList.get(i - 1).val){
                counter = 1;
                cost = arrayList.get(i).cost;
            }
            else {
                ++counter;
                cost += arrayList.get(i).cost;
            }
        }
        if(counter >= k){
            ans = Math.min(ans, cost);
        }
        writer.println(ans);
        writer.close();
    }
}