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.io.IOException
import java.io.InputStreamReader
import java.util.*
import kotlin.math.*

fun main() {
    var fs = Atcoder.FastReader()
    var x = fs.nextLong()
    var k = fs.nextLong()
    var d = fs.nextLong()
    x = abs(x)
    if (x / d > k) {
        println(x - k * d)
    } else {
        x -= ((x/d) *d).also { k -= x/d }
        if(k%2==0L) println(abs(x))
        else println(abs(abs(x)-d))
    }
}

class Atcoder {
    internal class FastReader {
        private var br: BufferedReader = BufferedReader(InputStreamReader(System.`in`))
        private var st: StringTokenizer? = null

        operator fun next(): String {
            while (st == null || !st!!.hasMoreElements()) {
                try {
                    st = StringTokenizer(br.readLine())
                } catch (e: IOException) {
                    e.printStackTrace()
                }

            }
            return st!!.nextToken()
        }

        fun nextInt(): Int {
            return Integer.parseInt(next())
        }

        fun nextLong(): Long {
            return java.lang.Long.parseLong(next())
        }

        fun nextDouble(): Double {
            return java.lang.Double.parseDouble(next())
        }

        fun nextLine(): String {
            var str = ""
            try {
                str = br.readLine()
            } catch (e: IOException) {
                e.printStackTrace()
            }
            return str
        }

        fun readIntArray(n: Int): IntArray {
            val a = IntArray(n)
            for (i in 0 until n) a[i] = nextInt()
            return a
        }

        fun readLongArray(n: Int): LongArray {
            val a = LongArray(n)
            for (i in 0 until n) a[i] = nextLong()
            return a
        }

        fun readDoubleArray(n: Int): DoubleArray {
            val a = DoubleArray(n)
            for (i in 0 until n) a[i] = nextDouble()
            return a
        }
    }
}