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 sys
input = sys.stdin.readline
from collections import defaultdict
from heapq import *

n, k = map(int, input().split())
a = list(map(int, input().split()))
pqs = defaultdict(list)

for i in range(n):
    ai = a[i]
    cnt = 0
    
    while True:
        if len(pqs[ai])<k:
            heappush(pqs[ai], -cnt)
        else:
            if -pqs[ai][0]>cnt:
                heappop(pqs[ai])
                heappush(pqs[ai], -cnt)
        
        if ai==0:
            break
        
        ai //= 2
        cnt += 1

ans = 10**18

for pq in pqs.values():
    if len(pq)<k:
        continue
    
    ans = min(ans, -sum(pq))

print(ans)