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.IOException;
import java.io.InputStream;
import java.util.Arrays;


public class EqualizingbyDivison {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input =new Scanner(System.in);
		int n = input.nextInt();
		int k = input.nextInt();
		pair[] vv =new pair[n*20];
		int m=0;
		for(int i=0; i<n;i++){
			int a = input.nextInt();
			for(int c=0;;c++){
				vv[m++] = new pair(a,c);
			
				if(a==0)break;
			    a = a/2;
			   
			}
			
		}
		Arrays.sort(vv, 0, m, (u, v) -> u.a != v.a ? u.a - v.a : u.b - v.b);
		int i=0;
		int ans = n*20;
		while(i<m){
			int j = i+1;
			while(j<m && vv[j].a == vv[i].a)j++;
			if(j-i>=k){
				int c = 0;
				for(int h=0; h<k;h++){
					c+=vv[i+h].b;
					
				}
				ans = Math.min(ans,c);
			}
			i=j;
		}
		System.out.println(ans);
		
		
	}

	static int log(int n){
		return (int)(Math.log(n)/Math.log(2));
	}
	static class Scanner {
		Scanner(InputStream in) { this.in = in; } InputStream in;
		int k, l; byte[] bb = new byte[1 << 15];
		byte getc() {
			if (k >= l) {
				k = 0;
				try { l = in.read(bb); } catch (IOException e) { l = 0; }
				if (l <= 0) return -1;
			}
			return bb[k++];
		}
		int nextInt() {
			byte c = 0; while (c <= 32) c = getc();
			int a = 0;
			while (c > 32) { a = a * 10 + c - '0'; c = getc(); }
			return a;
		}
		int m = 1 << 7; byte[] cc = new byte[m];
		int read() {
			byte c = 0; while (c <= 32) c = getc();
			int n = 0;
			while (c > 32) {
				if (n == m) cc = Arrays.copyOf(cc, m <<= 1);
				cc[n++] = c; c = getc();
			}
			return n;
		}
		byte[] nextBytes() { int n = read(); return Arrays.copyOf(cc, n); }
	}

	static class pair{
		int a;
		int b;
		
		public pair(int x, int y){
			a  = x;
			b = y;
		}
	}

}