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B. Roma and Changing Signs

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRoma 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.

Input

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.

Output

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

Examples

Input

3 2

-1 -1 1

Output

3

Input

3 1

-1 -1 1

Output

1

Note

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.

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