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:
/*
 *
 * @Author  Ajudiya_13(Bhargav Girdharbhai Ajudiya)
 * Dhirubhai Ambani Institute of Information And Communication Technology
 *
 */


import java.util.*;
import java.io.*;
import java.lang.*;

public class Code87
{

    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int test_case = 1;
        for(int t=0;t<test_case;t++)
        {
            int n = in.nextInt();
            int k = in.nextInt();
            int max = 200005;
            ArrayList<Integer> arrayList[] = new ArrayList[max];
            for(int i=0;i<max;i++)
                arrayList[i] = new ArrayList<>();
            for(int i=0;i<n;i++){
                int x = in.nextInt();
                arrayList[x].add(0);
                int count = 1;
                while(x>0){
                    int next = x/2;
                    arrayList[next].add(count);
                    x = next;
                    count++;
                }
            }
            int min = Integer.MAX_VALUE;

            for(int i=0;i<max;i++){
                if(arrayList[i].size()>=k){
                    Collections.sort(arrayList[i]);
                    int curSum = 0;
                    for(int j=0;j<k;j++)
                        curSum += arrayList[i].get(j);
                    min = Math.min(min, curSum);
                }
            }

            pw.print(min);
        }
        pw.flush();
        pw.close();
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

    public static long mod = 1000000007;
    public static int d;
    public static int p;
    public static int q;

    public static int[] suffle(int[] a,Random gen)
    {
        int n = a.length;
        for(int i=0;i<n;i++)
        {
            int ind = gen.nextInt(n-i)+i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static void swap(int a, int b){
        int temp = a;
        a = b;
        b = temp;
    }

    public static HashSet<Integer> primeFactorization(int n)
    {
        HashSet<Integer> a =new HashSet<Integer>();
        for(int i=2;i*i<=n;i++)
        {
            while(n%i==0)
            {
                a.add(i);
                n/=i;
            }
        }
        if(n!=1)
            a.add(n);
        return a;
    }

    public static void sieve(boolean[] isPrime,int n)
    {
        for(int i=1;i<n;i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for(int i=2;i*i<n;i++)
        {
            if(isPrime[i] == true)
            {
                for(int j=(2*i);j<n;j+=i)
                    isPrime[j] = false;
            }
        }
    }

    public static int GCD(int a,int b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }

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

    public static void extendedEuclid(int A,int B)
    {
        if(B==0)
        {
            d = A;
            p = 1 ;
            q = 0;
        }
        else
        {
            extendedEuclid(B, A%B);
            int temp = p;
            p = q;
            q = temp - (A/B)*q;
        }
    }

    public static long LCM(long a,long b)
    {
        return (a*b)/GCD(a,b);
    }

    public static int LCM(int a,int b)
    {
        return (a*b)/GCD(a,b);
    }

    public static int binaryExponentiation(int x,int n)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }

    public static long binaryExponentiation(long x,long n)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }

    public static int modularExponentiation(int x,int n,int M)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }

    public static long modularExponentiation(long x,long n,long M)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }

    public static int modInverse(int A,int M)
    {
        return modularExponentiation(A,M-2,M);
    }

    public static long modInverse(long A,long M)
    {
        return modularExponentiation(A,M-2,M);
    }

    public static boolean isPrime(int n)
    {

        if (n <= 1)  return false;
        if (n <= 3)  return true;

        if (n%2 == 0 || n%3 == 0)
            return false;

        for (int i=5; i*i<=n; i=i+6)
        {
            if (n%i == 0 || n%(i+2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>
    {
        Integer x, y;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }

        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = y.compareTo(o.y);

            return result;
        }

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

        public boolean equals(Object o)
        {
            if (o instanceof pair)
            {
                pair p = (pair)o;
                return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
            }
            return false;
        }

        public int hashCode()
        {
            return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    }
}