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.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;
public class D2EqualizingbyDivision {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n = in.nextInt();
        int k = in.nextInt();
        int mx = (int)(2e5);
        int mn = (int)(9e9);
        int []num = new int[mx+1];
        int []num2 = new int[mx+1];
        int []cost = new int[mx+1];
        for(int i=0;i<n;i++){
            int next = in.nextInt();
            num[next]++;
            num2[next]++;
        }
        for(int i=2;i<=mx;i++){
            if(num2[i]>0){
                int cur =i;int step=0;
                while (cur!=1){
                    step++;
                    cur>>=1;
                    if(num[cur]<k){
                        int take = Math.min(k-num[cur],num2[i]);
                        num[cur]+=take;
                        cost[cur]+=take*step;
                    }
                }
            }
        }
        for(int i=0;i<=mx;i++){
            if(num[i]>=k){
                mn = Math.min(mn,cost[i]);
            }
        }
        System.out.println(mn);

    }
}