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: Accepted)

import java.io.BufferedReader
import java.util.*
import kotlin.math.absoluteValue
import kotlin.math.min

fun main() = abc175c()

@OptIn(ExperimentalStdlibApi::class)
fun abc175c() = SimpleFastIOWithToken_abc175c().exec {
    val (x, moveCount, moveDist) = List(3) { readLong() }

    var currentPosition = x.absoluteValue
    var remainMoves = moveCount

    val moves = min(currentPosition / moveDist, moveCount)
    currentPosition -= moves * moveDist
    remainMoves -= moves

    val answer = if (remainMoves % 2 == 0L) currentPosition else moveDist - currentPosition

    println(answer)
}

// region kokokara template dayo (^o^)
@Suppress("unused", "HasPlatformType", "MemberVisibilityCanBePrivate", "ClassName")
private class SimpleFastIOWithToken_abc175c(private val separator: String = System.lineSeparator()) {
    private val br: BufferedReader = System.`in`.bufferedReader()
    private var st: StringTokenizer = StringTokenizer("")
    private val sb: StringBuilder = StringBuilder()
    private fun prepareNext() = run { if (!st.hasMoreTokens()) st = StringTokenizer(br.readLine()) }

    fun readString(): String = run { prepareNext() }.run { st.nextToken() }
    fun readInt(): Int = Integer.valueOf(readString())
    fun readLong(): Long = java.lang.Long.valueOf(readString())

    fun println(): Unit = run { sb.append(separator) }
    fun print(any: Any): Unit = run { sb.append(any) }
    fun println(any: Any): Unit = run { sb.append(any.toString() + separator) }

    fun exec(action: SimpleFastIOWithToken_abc175c.() -> Unit) {
        var t: Throwable? = null
        Thread(null, { action() }, "solve", 128 * 1024 * 1024)
            .apply { setUncaughtExceptionHandler { _, t1 -> t = t1 } }
            .apply { start() }.join()
        t?.let { throw it }
        kotlin.io.print(sb)
    }

    fun readLine(): Nothing = error("readLine is disabled.")
}
// endregion kokomade template dayo (^o^)