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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)
	defer out.Flush()

	x, k, d := nextInt(), nextInt(), nextInt()
	if x < 0 {
		x = x * (-1)
	}
	var checker float64
	checkK := x / d
	if checkK > k {
		checker = math.Abs(float64(x) - float64(k)*float64(d))
	} else {
		first := math.Abs(float64(x) - float64(checkK)*float64(d))
		second := math.Abs(float64(x) - float64(checkK+1)*float64(d))
		if (k-checkK)%2 == 0 {
			checker = first
		} else {
			checker = second
		}
	}
	fmt.Fprintf(out, "%d\n", int(checker))
}

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

func nextFloat64() float64 {
	a, _ := strconv.ParseFloat(next(), 64)
	return a
}

func reverse(s string) string {
	runes := []rune(s)
	for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
		runes[i], runes[j] = runes[j], runes[i]
	}
	return string(runes)
}

func quickSort(val []int) []int {
	if len(val) < 2 {
		return val
	}

	pivot := val[0]

	left := []int{}
	right := []int{}

	for _, v := range val[1:] {
		if pivot > v {
			left = append(left, v)
		} else {
			right = append(right, v)
		}
	}

	left = quickSort(left)
	right = quickSort(right)

	ret := append(left, pivot)
	ret = append(ret, right...)

	return ret
}