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.util.*;
//_________________________________________________________________
public class Main {
    public static void main(String[] args) throws IOException {
        File file = new File("input.txt");
        FastScanner sc = new FastScanner();
//                Scanner sc= new Scanner(file);
        PrintWriter out = new PrintWriter(System.out);
//        int t=sc.nextInt();
//        outer:while (t-->=1) {
//
//        }
        int n=sc.nextInt(),k=sc.nextInt();
        int a[]=sc.readArray(n);
        int m=(int)2e5+1;
        ArrayList<Integer> list[]= new ArrayList[m];
        for (int i=0;i<m;i++){
            list[i]= new ArrayList<>();
        }
        for (int i=0;i<n;i++){
            int x=a[i];
            int c=0;
            while (x>0){
                list[x].add(c);
                x/=2;
                c++;
            }
        }
//        for (int i=0;i<n;i++){
//            for (int j=0;j<list[i].size();j++) {
//                System.out.print(list[i].get(j) + " ");
//            }
//            System.out.println();
//        }
        int ans=Integer.MAX_VALUE;
        for (int i=0;i<m;i++){
            if (list[i].size()>=k){
                Collections.sort(list[i]);
                int sum=0;
                for (int j=0;j<k;j++){
                    sum+=list[i].get(j);
                }
//                System.out.println(sum);
                ans=Math.min(sum,ans);
            }
        }
        System.out.println(ans);
        out.flush();
    }
    //------------------------------------if-------------------------------------------------------------------------------------------------------------------------------------------------
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static String sortString(String s) {
        char temp[] = s.toCharArray();
        Arrays.sort(temp);
        return new String(temp);
    }
    static class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
//        to sort first part
                    public int compareTo(Pair other) {
                if (this.a == other.a) return other.b > this.b ? -1 : 1;
                else if (this.a > other.a) return 1;
                else return -1;
            }
//        public int compareTo(Pair other) {
//            if (this.b == other.b) return 0;
//            if (this.b < other.b) return 1;
//            else return -1;
//        }
        //sort on the basis of first part only
//        public int compareTo(Pair other) {
//            if (this.a == other.a) return 0;
//            else if (this.a > other.a) return 1;
//            else return -1;
//        }

    }
    static int[] frequency(String s){
        int fre[]= new int[26];
        for (int i=0;i<s.length();i++){
            fre[s.charAt(i)-'a']++;
        }
        return fre;
    }
    static int mod =(int)1e9;
    static long mod(long x) {
        return ((x % mod + mod) % mod);
    }
    static long add(long x, long y) {
        return mod(mod(x) + mod(y));
    }
    static long mul(long x, long y) {
        return mod(mod(x) * mod(y));
    }
    static int[] find(int n, int start, int diff) {
        int a[] = new int[n];
        a[0] = start;
        for (int i = 1; i < n; i++) a[i] = a[i - 1] + diff;
        return a;
    }
    static void swap(int a, int b) {
        int c = a;
        a = b;
        b = c;
    }
    static void printArray(int a[]) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
    }
    static boolean sorted(int a[]) {
        int n = a.length;
        boolean flag = true;
        for (int i = 0; i < n - 1; i++) {
            if (a[i] > a[i + 1]) flag = false;
        }
        if (flag) return true;
        else return false;
    }
    public static int findlog(long n) {
        if (n == 0)
            return 0;

        if (n == 1)
            return 0;
        if (n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if (den == 0)
            return 0;
        return (int) (num / den);
    }
    public static long gcd(long a, long b) {
        if (b % a == 0)
            return a;
        return gcd(b % a, a);
    }
    public static int gcdInt(int a, int b) {

        if (b % a == 0)
            return a;

        return gcdInt(b % a, a);

    }
    static void sortReverse(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        //        Collections.sort.(l);
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

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

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readArrayLong(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

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