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 math


n, k = map(int, input().split())
numbers = list(map(int, input().split()))
divisors = set()
divisors.add(0)
numbers.sort(reverse=True)
for p in range(18):
    m = 2 ** p
    for v in numbers:
        while v > 0:
            divisors.add(v)
            v //= 2
answer = 2 ** 64
for d in divisors:
    cnt = []
    for v in numbers:
        cur = 0
        while v > 0 and v != d:
            v //= 2
            cur += 1
        if v == d:
            cnt.append(cur)
    cnt.sort()
    if len(cnt) >= k:
        answer = min(answer, sum(cnt[:k]))
print(answer)