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.IOException
import java.lang.NumberFormatException
import java.lang.StringBuilder
import kotlin.math.absoluteValue
import kotlin.math.min

object CMain{
    fun solve(){
        val x = nextLong().absoluteValue
        val k = nextLong()
        val d = nextLong()

        if(x / k >= d){
            println(x - k * d)
        }else{
            val rem = k - x / d
            if(rem % 2 == 0L){
                println(x % d)
            }else{
                println(d - x % d)
            }
        }
    }





    // Scanner based on uwi-san's Java code
    val stream = System.`in`
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0

    fun hasNextByte(): Boolean{
        if(ptr < buflen){
            return true
        }else{
            ptr = 0
            try{
                buflen = stream.read(buffer)
            }catch (e: IOException){
                e.printStackTrace()
            }
            if(buflen <= 0){
                return false
            }
        }
        return true
    }

    fun readByte() =
        if(hasNextByte()) buffer[ptr++]
        else -1

    fun isPrintableChar(c: Byte) = c in 33..126

    fun hasNext(): Boolean{
        while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++
        return hasNextByte()
    }

    fun next(): String{
        if(!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while(isPrintableChar(b)){
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun nextLong(): Long{
        if(!hasNext()) throw NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if(b == '-'.toByte()){
            minus = true
            b = readByte()
        }
        if(b !in '0'.toByte()..'9'.toByte())
            throw NumberFormatException()
        while(true){
            if(b in '0'.toByte()..'9'.toByte()){
                n *= 10
                n += b - '0'.toByte()
            }else if(!isPrintableChar(b)){
                return if(minus) -n else n
            }else{
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextInt(): Int{
        val n1 = nextLong()
        if(n1 !in Int.MIN_VALUE..Int.MAX_VALUE)
            throw NumberFormatException()
        return n1.toInt()
    }

    fun NextDouble() = next().toDouble()
}

fun main(){
    CMain.solve()
}