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 PYTHON):

Solution:
q = map(int,raw_input().split())
l = map(int,raw_input().split())
n = q[0]
k = q[1]
res = 0
ls = list(set(l))
nus = []
for i in ls:
    nus.append(l.count(i))

l = sorted(l)
res=20000000000000
for i in range(200000):
    tmp = 0
    tmpadim = 0
    for j in l:
        g = 0
        a = j
        while(a>i):
            a/=2
            g+=1
        if a == i:
            tmp+=1
            tmpadim += g
        if tmp==k:
            res = min(res,tmpadim)
            break
        

print res