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

di = {}
cdi = {}

for el in a:
    cdi[el] = 1 if el not in cdi else cdi[el]+1


for el in a:
    ec = el
    di[ec] = [0] if ec not in di else di[ec] + [0]
    lis = [el]
    count = 0
    ec2 = ec
    while ec2 != 0:
        ec2 = ec // (2**(count+1))
        count += 1
        di[ec2] = [count] if ec2 not in di else di[ec2] + [count]
    #print(di)


ans = 9999999999999999999999999999999
for all in di:
    nextlis = di[all]
    if len(nextlis) < k:
        continue
    #print(all, nextlis)
    nextlis = sorted(nextlis)[:k]
    ans = min(sum(nextlis), ans)
print(ans)