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:

# -*- coding: utf-8 -*-
# @Date    : 2019-08-31 10:31:50
# @Author  : raj lath (oorja.halt@gmail.com)
# @Link    : link
# @Version : 1.0.0

import sys
sys.setrecursionlimit(10**5+1)

inf     =  int(10 ** 20)
max_val =  inf
min_val = -inf

RW  = lambda : sys.stdin.readline().strip()
RI  = lambda : int(RW())
RMI = lambda : [int(x) for x in sys.stdin.readline().strip().split()]
RWI = lambda : [x for x in sys.stdin.readline().strip().split()]

from collections import defaultdict
n, k = RMI()
vals = RMI()
valids = defaultdict(list)
for i in vals:
    has = 0
    while i != 0:
        valids[i].append(has)
        has += 1
        i//=2
mins = max_val
for i in valids.values():
    if len(i) >= k:
        i.sort()
        mins = min(mins, sum(i[:k]))
print(mins)