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.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class EqualizingByDivision {
    static class Number {
        int number;
        int k;
        int minOperations;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int k = scanner.nextInt();

        int[] a = new int[n];

        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        Arrays.sort(a);

        Map<Integer, Number> map = new HashMap<>();
        long minOperations = Long.MAX_VALUE;

        for (int i = 0; i < n; i++) {
            int numberOfOperations = 0;
            int zeroCount = 0;

            while (a[i] >= 0 && zeroCount < 2) {
                if (map.containsKey(a[i])) {
                    Number number = map.get(a[i]);

                    if (number.k == k) {

                    }
                    else {
                        number.minOperations += numberOfOperations;
                        number.k = number.k + 1;
                        if (number.k == k) {
                            if (number.minOperations < minOperations)
                                minOperations = number.minOperations;
                        }
                    }
                }
                else {
                    Number number = new Number();
                    number.number = a[i];
                    number.k = 1;
                    number.minOperations = numberOfOperations;
                    map.put(a[i], number);

                    if (k == 1) {
                        if (number.minOperations < minOperations)
                            minOperations = number.minOperations;
                    }
                }

                a[i] /= 2;
                numberOfOperations++;

                if (a[i] == 0)
                    zeroCount++;
            }

        }

        System.out.println(minOperations);
    }
}