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 collections import defaultdict

hash1 = defaultdict(int)

hash2 = defaultdict(list)


n,k = map(int,input().split())


l = list(map(int,input().split()))

l.sort()
ans = 10**18
for i in l:

    j = i
    count = 0
    while True:

        hash2[j].append(count)
        if j == 0:
            break
        j//=2
        count+=1

for i in hash2.keys():
  if len(hash2[i])>=k:
    hash2[i].sort()
    ans = min(ans,sum(hash2[i][:k]))

print(ans)