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.*;
import java.io.*;
import java.math.BigInteger;
public class b{

	public static void main( String [] args) throws IOException{
	  BufferInput sc=new BufferInput();
	  int n=sc.nextInt();
	  int k=sc.nextInt();
	  int [] a=sc.nextIntArray(n);
	  Set<Integer> set=new HashSet<>();
	  for(int i : a){
		  int x=i;
		  while(x>0){
			  set.add(x);
			  x/=2;
		  }
	  }
	  set.add(0);

	  int min=Integer.MAX_VALUE;
	  Iterator it=set.iterator();
	  while(it.hasNext()){
		List<Integer> move=new ArrayList<>();
		  int x=(int)it.next();
		  for(int i=0;i<n;i++){
			  int cnt=0;
			  int y=a[i];
			  while(y>x){
				  y/=2;cnt++;
			  }
			  if(y==x){
				  move.add(cnt);
			  }
		  }
		  if(move.size()<k)continue;
		  move.sort((aa,bb)->aa-bb);
		  int sum=0;
		  for(int i=0;i<k;i++)sum+=move.get(i);
		  min=Math.min(sum,min);
	  }

	  System.out.println(min);

	}
}



























































































class BufferInput{	
	 private int BUFFER_SIZE = 1 << 16;
	
	private  DataInputStream din;
	
	private  byte[] buffer;
	
	private int bufferPointer, bytesRead;
	
	public BufferInput() {
		din = new DataInputStream(System.in);
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}

	public BufferInput( String file_name) throws IOException {
		din = new DataInputStream(new FileInputStream(file_name));
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
    }
    
	public String readLine() throws IOException {
		 byte[] buf = new byte[64];
		int cnt = 0, c;
		while ((c = read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}
    
    public String next() throws IOException{

		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		
		 StringBuilder builder = new StringBuilder();
		builder.append((char)c);
		c = read();
		while(!Character.isWhitespace(c)){
			builder.append((char)c);
			c = read();
		}
		
		return builder.toString();
	}

	public int nextInt() throws IOException {
		int ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (neg)
			return -ret;
		return ret;
	}
	
	public int[] nextIntArray( int n) throws IOException {
		 int arr[] = new int[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextInt();
		}
		return arr;
	}

	public long nextLong() throws IOException {
		long ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}
	
	public long[] nextLongArray( int n) throws IOException {
		 long arr[] = new long[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextLong();
		}
		return arr;
	}

	public char nextChar() throws IOException{
		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		return (char) c;	
	}
	
	public double nextDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg)
			return -ret;
		return ret;
    }
    
	public double[] nextDoubleArray( int n) throws IOException {
		 double arr[] = new double[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextDouble();
		}
		return arr;
	}

	private void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private byte read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	public void close() throws IOException {
		if (din == null)
			return;
		din.close();
	}

}