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 PYTHON3):

Solution:
'''
 Author: fuad Ashraful Mehmet
 University of Asia Pacific
 created :30 Aug 2019 7.33 PM
 Category :   from Code Forces

 Problem:https:  hala onk para disa 2 din 
'''

 

n,k=map(int,input().split())


fuad=list(map(int,input().split()))

fuad.sort()


steps={}
num={}
ans=200000000
for a in fuad:

	cnt=0
	x=a
	while 1:
		num[x]=num.get(x,0)+1
		steps[x]=steps.get(x,0)+cnt
		cnt+=1
		if(num[x]==k):
			ans=min(ans,steps[x])

		x//=2
		if x==0:
			break



print(ans)