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
###############################################################
def iinput(): return int(stdin.readline())
def minput(): return map(int, stdin.readline().split())
def linput(): return list(map(int, stdin.readline().split()))
###############################################################

n, k = minput()
a = linput()
a.sort()
mn = float('inf')
p = []
for i in range(n):
    temp = a[i]
    while temp:
        p.append(temp)
        temp//=2

p = list(set(p))
for i in range(len(p)):
    c = p[i]
    op = []
    for j in range(n):
        cnt = 0
        temp = a[j]
        while temp > c:
            temp //= 2
            cnt += 1
        if temp == c:
            op.append(cnt)
    if len(op)>=k:
        op.sort()
        mn = min(mn, sum(op[:k]))


c = 0
for i in range(k):
    while a[i]:
        a[i]//=2
        c+=1
mn = min(mn, c)
print(mn)