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
from sys import setrecursionlimit as SRL; SRL(10**7)
rd = stdin.readline
rrd = lambda: map(int, rd().strip().split())

n,k = rrd()

a = list(rrd())

cnt = [0]*400005
a.sort()

for i in a:
    cnt[i] += 1

for i in range(400002):
    if i:
        cnt[i] += cnt[i-1]

mx = a[-1]

import math
ans = math.inf
for i in range(1,mx+1):

    now = k
    tot = 0
    l = i
    r = i
    st = 0

    while now:

        if l > 200000:
            tot = math.inf
            break

        p = min(cnt[r] - cnt[l-1],now)
        now -= p
        tot += st*p
        r = r*2+1
        l = l*2

        st += 1

    ans = min(ans,tot)



print(ans)