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

n, k = [int(i) for i in stdin.readline().strip().split()]
a = [int(i) for i in stdin.readline().strip().split()]


p = [19 * [0] for _ in range(max(a) + 1)]


nums = set()
for m in a:
    for i in range(19):
        p[m >> i][i] += 1
        nums.add(m >> i)

        if (m >> i) == 0:
            break

res = 10000000000000000000

for m in nums:
    d = p[m]
    sum = 0
    steps = 0
    for i in range(19):
        if sum + d[i] >= k:
            add = (k - sum) * i
            steps += add
            res = min(steps, res)
            break
        else:
            sum += d[i]
            steps += (i * d[i])

print(res)