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 (
	"fmt"
)

func abs(n int64) int64 {
	if n >= 0 {
		return n
	} else {
		return (-1) * n
	}
}

func main() {
	var x, k, d int64
	fmt.Scan(&x)
	fmt.Scan(&k)
	fmt.Scan(&d)
	ans := x

	if abs(x) > abs(k*d) {
		ans = abs(x) - abs(k*d)
	} else {
		if (k-abs(x)/abs(d))%2 == 0 {
			ans = abs(x) % abs(d)
		} else {
			temp := abs(x) % abs(d)
			if abs(temp+d) < abs(temp-d) {
				ans = abs(temp + d)
			} else {
				ans = abs(temp - d)
			}
		}
	}

	fmt.Println(abs(ans))
}