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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

/**
 * #
 *
 * @author pttrung
 */
public class D1_Round_582_Div3 {

    public static long MOD = 998244353;
    static int[][] dp;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int k = in.nextInt();
        int[] data = new int[n];

        for (int i = 0; i < n; i++) {
            data[i] = in.nextInt();
        }
        ArrayList<Point> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int cur = 0;
            int num = data[i];
            while (num > 0) {
                list.add(new Point(num, cur));
                num /= 2;
                cur++;
            }
            list.add(new Point(num, cur));

        }
        Collections.sort(list, (a, b) -> {
            if (a.x != b.x) {
                return Integer.compare(a.x, b.x);
            }
            return Integer.compare(a.y, b.y);
        });
        //System.out.println(list);
        int result = Integer.MAX_VALUE;
        for (int i = 0; i < list.size(); i++) {
            int ed = i + 1;
            int total = list.get(i).y;
            while (ed < list.size() && list.get(ed).x == list.get(i).x) {
                ed++;
                if (ed - i <= k) {
                    total += list.get(ed - 1).y;
                }
            }
            if (ed - i >= k) {
                //System.out.println(list.get(i).x);
                result = Integer.min(result, total);
            }
            i = ed - 1;
        }
        out.println(result);
        out.close();
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }

        public String toString(){
            return x + " " + y;
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * (val * a);

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}