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:
'''input
5 3
1 2 3 3 3
'''
from sys import stdin
from copy import deepcopy
from collections import deque


def solve(aux):
	# print(aux)

	count = 0
	for i in range(1, len(aux)):
		while  True:
			if aux[i] > aux[i - 1]:
				aux[i] //= 2
				count += 1
			elif aux[i] < aux[i - 1]:
				aux[i - 1] //= 2
				count += i
			else:
				break
	
	# print(count)
	return count


def get_arr(num, arr):
	aux = []
	for i in range(len(arr)):
		count = 0
		c = arr[i]
		while True:
			if c > num:
				c//= 2
				count += 1
			elif c < num:
				aux.append(float('inf'))
				break
			else:
				aux.append(count)
				break
	aux.sort()
	# print(num, aux)
	return aux


# main starts
n, k = list(map(int, stdin.readline().split()))
arr = list(map(int, stdin.readline().split()))
m = max(arr)
ans = float('inf')
for i in range(0, m + 1):
	aux = get_arr(i, arr)
	ans = min(ans, sum(aux[: k]))

print(ans)