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.lang.reflect.Array;
import java.math.*;
import java.util.*;

public class Main {
    static final long MOD = 998244353;
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner();
        int N = sc.nextInt();
        int K = sc.nextInt();
        //int N = 200000;
        //int K = 200000;
        ArrayList<Integer> nums = new ArrayList();
        for (int i = 0; i < N; i++) {
            nums.add(sc.nextInt());
            //nums[i] = 200000;
        }
        //long t1 = System.currentTimeMillis();
        Collections.sort(nums);
        int[] sumToHit = new int[200001];
        int[] Kleft = new int[200001];
        for (int i = 0; i <= 200000; i++) {
            Kleft[i] = K;
        }

        for (int num: nums) {
            int key = num;
            int steps = 0;
            while (key > 0) {
                if (Kleft[key] > 0) {
                    sumToHit[key] += steps;
                    Kleft[key] -= 1;
                }
                key = key/2;
                steps++;
            }
            if (Kleft[0] > 0) {
                sumToHit[0] += steps;
                Kleft[0] -= 1;
            }
        }

        int bestCost = Integer.MAX_VALUE;
        for (int i = 0; i <= 200000; i++) {
            if (Kleft[i] == 0) {
                bestCost = Math.min(bestCost, sumToHit[i]);
            }
        }
        System.out.println(bestCost);
        //long t2 = System.currentTimeMillis();
        //System.out.println(t2-t1);
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}

class Node {
    public int n;
    public HashSet<Node> children;

    public Node(int n) {
        this.n = n;
        children = new HashSet<Node>();
    }

    public void addChild(Node node) {
        children.add(node);
    }
}

class BinaryIndexedTree {
    public long[] arr;

    public BinaryIndexedTree (int N) {
        arr = new long[N+1];
        arr[0] = 0;
    }

    //add k to the i-th element.
    public void add(long k, int i) {
        int node = i+1;
        while (node < arr.length) {
            arr[node] += k;
            node += node & (-node);
        }
    }

    //sum up the elements from input[s_i] to input[e_i], from [s_i,e_i).
    public long sum(int s_i, int e_i) {
        return sum(e_i) - sum(s_i);
    }

    public long sum(int i) {
        long total = 0;
        int node = i;
        while (node > 0) {
            total += arr[node];
            node -= node & (-node);
        }
        return total;
    }
}