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.*
import java.util.*
import java.io.*
var ans:Long = 0L
var maxmove:Long = 0L
var xplus:Long = 0L
var xminus:Long = 0L
var Kevenorodd:Long = 0
var xrest:Long = 0
fun main() {
    val N = readLine()!!.split(" ").map { it.toLong() }
    val X:Long = N[0].absoluteValue
    val K:Long = N[1]
    val D:Long = N[2]

    Kevenorodd = K%2L
    maxmove = K * D

    if(X == 0L){
        if(Kevenorodd == 0L){
            ans = 0
        }
        else{
            ans = D
        }
    }
    else if(X < D){
        if(Kevenorodd == 0L){
            ans =X
        }
        else{
            ans = (X-D).absoluteValue
        }
    }
    else{
        xrest = (X/D)%2L
        if(X >= maxmove){
            ans = X - maxmove
        }
        else{
            xplus = X%D
            xminus = (xplus - D).absoluteValue
            if(xrest == Kevenorodd){
                ans = xplus
            }
            else{
                ans = xminus
            }
        }
    }

    println(ans)
}