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:
import math
import sys
from heapq import heappop
from heapq import heappush
from heapq import heapify
from bisect import insort
from sys import stdin,stdout
from collections import defaultdict

inp=lambda : int(stdin.readline())
sip=lambda : input()
mulip =lambda : map(int,input().split())
lst=lambda : list(map(int,stdin.readline().split()))
slst=lambda: list(sip())
arr2d= lambda x: [[int(j) for j in input().split()] for i in range(x)]
odds = lambda l: len(list(filter(lambda x: x%2!=0, l)))
evens = lambda l: len(list(filter(lambda x: x%2==0, l)))
mod = pow(10,9)+7
#-------------------------------------------------------
n, k = map(int, input().split())
A = [int(x) for x in input().split()]
vals = defaultdict(list)
for i in range(n):
    x = A[i]
    cnt = 0 
    while(x>0):
        vals[x].append(cnt)
        #print(x,":",vals[x])
        x = x//2
        cnt+=1

res = pow(10,10)
for i in range(2*pow(10,5)+1):
    l = vals[i] 
    l = sorted(l)
    if len(l)>=k:
        res = min(res, sum(l[:k]))

print(res)