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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class CF {

    public static void updateMap(HashMap<Integer, Integer>levels, HashMap<Integer, Integer>levelSum, int num, int count, int maxSimilar){
        if(levels.containsKey(num)){
            if(levels.get(num) < maxSimilar){
                levels.put(num, levels.get(num) + 1);
                levelSum.put(num, levelSum.get(num) + count);
            }
        } else {
            levels.put(num, 1);
            levelSum.put(num, count);
        }
    }
    public static void main(String[] args) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());

        Integer array[] = new Integer[n + 1];
        st = new StringTokenizer(br.readLine());
        
        array[0] = 0;
        
        for(int i = 1;i <= n;i++){
            array[i] = Integer.parseInt(st.nextToken());
        }

        Arrays.sort(array);

        HashMap<Integer, Integer>levels = new HashMap<>();
        HashMap<Integer, Integer>levelSum = new HashMap<>();

        for(int i = 1;i <= n;i++){
            int count = 0;
            while(array[i] > 0){
                updateMap(levels, levelSum, array[i], count, k);
                array[i] /= 2;
                count++;
            }
        }
        int ans = Integer.MAX_VALUE / 2;
        for(Integer key : levels.keySet()){
            if(levels.get(key) == k){
                ans = Math.min(ans, levelSum.get(key));
            }
        }

        System.out.println(ans);
    }
}