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 main(){
	var x, k, d int
	fmt.Scan(&x, &k, &d)


	if x == 0 {
		if k % 2 == 0 {
			fmt.Println(0)
			return
		}
		fmt.Println(d)
		return
	}
	x = abs(x)
	ans := x % d
	a := x / d
	if a > k {
		// 往復に辿り着く前に終る
		if x > 0  {
			fmt.Println(abs(x - k * d))
			return
		} else if  x < 0 {
			fmt.Println(abs(x +  k * d))
			return
		}
	} else if a <= k  {
		// 往復する
		if (k - a) % 2 == 0 {
			fmt.Println(abs(ans))
			return
		} else if (k-a) % 2 == 1 {
			if ans > 0 {
				ans -= d
			} else {
				ans += d
			}
			fmt.Println(abs(ans))
			return
		}
	}
}

func abs(n int) int {
	y := n >> 63
	return (n ^ y) - y
}