Problem:
Score : 300 points

Problem Statement

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

-10^{15} \leq X \leq 10^{15}

1 \leq K \leq 10^{15}

1 \leq D \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X K D

Output

Print the minimum possible absolute value of the coordinate of the destination.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input) {
    input = input.split(" ");
    result = [];

    for (i in input) {
        input[i] = Number(input[i]);
    }

    input[0] = Math.abs(input[0]);
    if (input[0] > input[1] * input[2]) {
        console.log(input[0] - input[1] * input[2]);
    } else {
        if (
            Math.round(input[0] / input[2]) % 2 == input[1] % 2 ||
            (input[0] / input[2]) % 1 == 0.5
        ) {
            console.log(
                Math.abs(input[0] - input[2] * Math.round(input[0] / input[2]))
            );
        } else {
            if (input[0] - input[2] * Math.round(input[0] / input[2] + 1) < 0) {
                console.log(
                    Math.abs(
                        input[0] -
                            input[2] * Math.round(input[0] / input[2] + 1)
                    )
                );
            } else {
                console.log(
                    Math.abs(
                        input[0] -
                            input[2] * (Math.round(input[0] / input[2]) - 1)
                    )
                );
            }
        }
    }
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));