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.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[] nums = new int[N];
        for (int i = 0; i < N; i++)
        	nums[i] = sc.nextInt();
        Arrays.sort(nums);
        Num[] targets = new Num[nums[N-1]+1];
        for (int i = 0; i < targets.length; i++) {
        	targets[i] = new Num(i);
        }
        int[] sumToHit = new int[targets.length];
        int[] Kleft = new int[targets.length];
        for (int i = 0; i < Kleft.length; i++) {
        	Kleft[i] = K;
        }
        
        for (int num: nums) {
        	for (int key: targets[num].reachable.keySet()) {
        		if (Kleft[key] > 0) {
        			sumToHit[key] += targets[num].reachable.get(key);
        			Kleft[key] -= 1;
        		}
        	}
        }
        
        int bestCost = Integer.MAX_VALUE;
        for (int i = 0; i < targets.length; i++) {
        	if (Kleft[i] == 0) {
        		bestCost = Math.min(bestCost, sumToHit[i]);
        	}
        }
        System.out.println(bestCost);
    }
    
    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;
	  }
}

class Num {
	public int n;
	public HashMap<Integer,Integer> reachable;
	
	public Num(int n) {
		this.n = n;
		reachable = new HashMap<Integer,Integer>();
		int temp = n;
		int steps = 0;
		while (temp > 0) {
			reachable.put(temp, steps);
			temp = temp/2;
			steps++;
		}
		reachable.put(0,steps);
	}
}