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 sys
from array import array  # noqa: F401
from typing import List, Tuple, TypeVar, Generic, Sequence, Union  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def main():
    from itertools import accumulate
    from collections import Counter
    n, k = map(int, input().split())
    a = sorted(map(int, input().split()))
    if Counter(a).most_common(1)[0][1] >= k:
        print(0)
        exit()
    acc = [0] + list(accumulate(a))

    ans = 10**18
    for i in range(n):
        if i >= k - 1:
            ans = min(ans, (a[i] - 1) * i - acc[i] + k - 1)
        if n - i - 1 >= k - 1:
            ans = min(ans, (acc[-1] - acc[i + 1]) - (a[i] + 1) * (n - i - 1) + k - 1)

        ans = min(
            ans,
            (a[i] - 1) * i - acc[i] + (acc[-1] - acc[i + 1]) - (a[i] + 1) * (n - i - 1) + k - 1
        )

    print(ans)


if __name__ == '__main__':
    main()