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 kotlin.math.absoluteValue
import kotlin.math.max
import kotlin.math.min

fun main() {
    val ln = nextLongList()
    val ans = solve(ln)
    println(ans)
}


fun solve(ln: List<Long>): Long {
    val current = ln[0]
    val moveCount = ln[1]
    val moveAmount = ln[2]

    if (current.absoluteValue == moveAmount) {
        return current.absoluteValue
    }

    //移動する必要がある
    if (current.absoluteValue > moveAmount / 2) {
        //実際に移動する回数
        val actualMoveCount = moveCount - current.absoluteValue / moveAmount
        if(actualMoveCount > 0) {
            return min(current - moveAmount * actualMoveCount, current + moveAmount * actualMoveCount).absoluteValue
        } else {
            return min(current - moveAmount * moveCount, current + moveAmount * moveCount).absoluteValue
        }

    } else {
        //移動回数が偶数である場合
        if (moveCount % 2 == 0L) {
            return current.absoluteValue
            //移動回数が奇数である場合
        } else {
            return min(current - moveAmount, current + moveAmount).absoluteValue
        }
    }
}

fun nextInt(): Int {
    return readLine()!!.toInt()
}

fun nextIntList(): List<Int> {
    return readLine()!!.split(" ").map { it.toInt() }
}

fun nextLongList(): List<Long> {
    return readLine()!!.split(" ").map { it.toLong() }
}

fun nextString(): String {
    return readLine()!!
}