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: Time Limit Exceeded)

package main

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

var (
	sc = bufio.NewReader(os.Stdin)
)

func main() {
	X := scanInt()
	K := scanInt()
	D := scanInt()

	MD := K * D
	// if MD <= absInt(X) {
	// 	fmt.Println(absInt(X) - MD)
	// 	return
	// }

	if MD > absInt(X) && X != 0 {
		t := absInt(X) / D
		K -= t
		if X < 0 {
			X += D * t
		} else {
			X -= D * t
		}
	}
	smallest := 1000000000000001
	history := []int{}
	for i := 0; i < K; i++ {
		a := absInt(X - D)
		b := absInt(X + D)
		if a < b {
			X -= D
		} else {
			X += D
		}
		history = append(history, absInt(X))
		if absInt(X) < smallest {
			smallest = absInt(X)
		} else {
			if i >= 2 && history[i] != history[i-2] {
				continue
			}
			if (K-i)%2 == 0 {
				fmt.Println(absInt(smallest))
			} else {
				fmt.Println(absInt(X))
			}
			return
		}
	}
	fmt.Println(absInt(X))
}

func absInt(a int) int      { return int(math.Abs(float64(a))) }
func scan(a ...interface{}) { _, err := fmt.Fscan(sc, a...); pnc(err) }
func scanStr() (s string)   { scan(&s); return }
func scanInt() int          { i, err := strconv.Atoi(scanStr()); pnc(err); return i }
func scanFloat() float64    { f, err := strconv.ParseFloat(scanStr(), 64); pnc(err); return f }
func pnc(err error) {
	if err != nil {
		panic(err)
	}
}