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:
from sys import stdin, stdout
from collections import Counter
import math
 
def rsingle_int():
    return int(stdin.readline().rstrip())
 
def rmult_int():
    return [ int(x) for x in stdin.readline().rstrip().split() ]
 
def rmult_str():
    return stdin.readline().rstrip().split()
 
def r_str():
    return stdin.readline().rstrip()
    
def rsingle_char():
    return stdin.read(1)

def sortFirst(val):
    return val[0]

def main():
    n, k = rmult_int()
    a = rmult_int()
    cnts = {}
    a.sort()
    for el in a:
        cnt = 0
        while el != 0:
            if el not in cnts:
                cnts[el] = []
            cnts[el].append(cnt)
            el = int(math.floor(el / 2))
            cnt += 1
        if el not in cnts:
            cnts[el] = []
        cnts[el].append(cnt)

    min_cost = float(math.inf)

    for el in cnts.keys():
        arr = cnts[el]
        if len(arr) >= k:
            sum_ = 0
            for i in range(k):
                sum_ += arr[i]
            if sum_ < min_cost:
                min_cost = sum_

    print(min_cost)


main()