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

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

        self.cnt


def main():
    # q = int(sys.stdin.readline().strip())
        # k = int(sys.stdin.readline().strip())
    n, m = [int(s) for s in sys.stdin.readline().strip().split()]
    xs = sorted(int(s) for s in sys.stdin.readline().strip().split())
    mmm = max(xs) + 1

    prefix = [0 for _ in range(mmm)]
    costs = [0 for _ in range(mmm)]
    for x in xs:
        c = 0
        while x > 0:
            if prefix[x] < m:
                costs[x] += c
            prefix[x] += 1
            c += 1
            x //= 2
        if prefix[0] < m:
            costs[0] += c
        prefix[0] += 1

    best = None
    for i in range(mmm):
        if prefix[i] >= m:
            s = costs[i]
            if best is None:
                best = s
            else:
                best = min(best, s)

    print(best)

main()