Roma works in a company that sells TVs. Now he has to prepare a report for the last year.

Roma has got a list of the company's incomes. The list is a sequence that consists of *n* integers. The total income of the company is the sum of all integers in sequence. Roma decided to perform exactly *k* changes of signs of several numbers in the sequence. He can also change the sign of a number one, two or more times.

The operation of changing a number's sign is the operation of multiplying this number by -1.

Help Roma perform the changes so as to make the total income of the company (the sum of numbers in the resulting sequence) maximum. Note that Roma should perform exactly *k* changes.
The first line contains two integers *n* and *k* (1 ≤ *n*, *k* ≤ 10<sup class="upper-index">5</sup>), showing, how many numbers are in the sequence and how many swaps are to be made.

The second line contains a non-decreasing sequence, consisting of *n* integers *a*<sub class="lower-index">*i*</sub> (|*a*<sub class="lower-index">*i*</sub>| ≤ 10<sup class="upper-index">4</sup>).

The numbers in the lines are separated by single spaces. Please note that the given sequence is sorted in non-decreasing order.
import sys

def mi(s):
    return map(int, s.strip().split())

def lmi(s):
    return list(mi(s))

def main(arr, k):
    arr.sort()
    negs = [i for i in arr if i < 0]
    pos = [i for i in arr if i >= 0]
    smallest_negs = negs[:len(negs) - k]
    largest_negs = list(map(lambda x: -x, negs[len(negs)-k:]))
    remaining = len(largest_negs) - k
    pos_flips = list(map(lambda x: -x, pos[:remaining]))
    r = pos[remaining:]
    return sum(smallest_negs) + sum(largest_negs) + sum(pos_flips) + sum(r)

if __name__ == "__main__":
    for e, line in enumerate(sys.stdin.readlines()):
        if e == 0:
            _, k = mi(line)
        else:
            colors = lmi(line)

    # Proof by induction that sorting is that
    # same as solving this problem.
    print(main(colors, k))
