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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.io.PrintWriter
import java.util.StringTokenizer
import kotlin.math.abs

fun main() {

    fun PrintWriter.solve() {
        var (x,k,d) = List(3){nextLong()}
        if(x >= 0){
            if (x >= k * d) {
                println("${x - k * d}")
            } else {
                val nk = x / d
                k -= nk
                x = x - nk * d
                if (k % 2 == 0L) {
                    println("${x}")
                } else {
                    println("${-(x - d)}")
                }
            }
        }
        else{
            if (x + k*d <= 0){
                println("${abs(x+k*d)}")
            }
            else{
                val nk = (-x)/d
                k -= nk
                if (k%2 == 0L){
                    println("${abs(x)}")
                }
                else{
                    println("${abs(x+d)}")
                }
            }
        }


    }

    writer.solve()
    writer.flush()


}


private val reader = System.`in`.bufferedReader()
private val writer = PrintWriter(System.out, false)

private var tokenizer: StringTokenizer = StringTokenizer("")

private fun next(): String {
    while (tokenizer.hasMoreTokens().not()) tokenizer = StringTokenizer(reader.readLine())
    return tokenizer.nextToken()
}

private fun nextInt() = next().toInt()
private fun nextLong() = next().toLong()
private fun nextDouble() = next().toDouble()
private fun nextLine() = reader.readLine()