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
import  java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner sca=new Scanner(System.in);
        int n=sca.nextInt();
        int k=sca.nextInt();
        int[] num=new int[n];
        int[] count=new int[200001];
        int[] counts =new int[200001];
        for (int i = 0; i < n; i++) {
            num[i]=sca.nextInt();
        }
        Arrays.sort(num);
        int con=0;
        for (int i = 0; i < n; i++) {
            int x=num[i],sum=0;
            while (x!=0){
                if(count[x]<k){
                    count[x]++;
                    counts[x]+=sum;
                }
                sum++;
                x /= 2;
            }
        }
        int a=200001;
        for (int i = 0; i < 200001; i++) {
            if(count[i]>=k){
                a=Integer.min(a,counts[i]);
            }
        }
        System.out.println(a);
    }
}

 			 			   	 			   			 		  		