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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

func abs(a int) int {
	return int(math.Abs(float64(a)))
}

func max(a, b int) int {
	return int(math.Max(float64(a), float64(b)))
}

func min(a, b int) int {
	return int(math.Min(float64(a), float64(b)))
}

func main(){
	var X, K, D int
	fmt.Scan(&X, &K, &D)

	if abs(X)/D >= K {
		if X > 0 {
			X -= D * K
		}else {
			X += D * K
		}
		fmt.Println(X)
		return
	}

	if abs(X)/D > 0 {
		K -= abs(X)/D
		if X > 0 {
			X -= (abs(X)/D) * D
		}else {
			X += (abs(X)/D) * D
		}
	}

	if K%2 == 0 {
		fmt.Println(X)
	}else{
		fmt.Println(min(abs(X-D), abs(X+D)))
	}
}