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 input():
    return next(stdin)

def main():
    n,k = map(int,input().split())
    aa = [int(a) for a in input().split()]
    aa.sort()
    valmap = {}
    for a in aa:
        add_to_map(a, 0, k, valmap)
        i = 0
        while a > 0:
            i+=1
            a = a//2
            add_to_map(a, i, k, valmap)

    result = min(s for c,s in valmap.values() if c == k)
    print(result)


def add_to_map(a, i, k, valmap):
    if a in valmap:
        if valmap[a][0] < k:
            valmap[a][0] += 1
            valmap[a][1] += i
    else:
        valmap[a] = [1, i]


if __name__ == "__main__":
    main()