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 PYTHON):

Solution:
#####################################   
import atexit, io, sys, collections, math, heapq, fractions, bisect,copy
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   

####################################



def g(ais,k):
	costs = collections.defaultdict(list)
	for ai in ais:
		cost = 0
		while(ai):
			costs[ai].append(cost)
			cost +=1
			ai /= 2
	ans = +float('inf')
	
	for key in costs:
		bi = costs[key]

		if len(bi) >= k:
			bi.sort()
			ans = min(ans, sum(bi[:k]))
	return ans
n,k = map(int ,raw_input().split())
print g(map(int,raw_input().split()), k)