A8795. Roma and Changing Signs

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 $k$ $(1<=n,k<=10^{5})$ , 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 $a_{i}$ $(|a_{i}|<=10^{4})$ .

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

In the single line print the answer to the problem — the maximum total income that we can obtain after exactly $k$ changes.

In the first sample we can get sequence \[1, 1, 1\], thus the total income equals $3$ .

In the second test, the optimal strategy is to get sequence \[-1, 1, 1\], thus the total income equals $1$ .