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 (
	"bufio"
	"fmt"
	"log"
	"math"
	"os"
	"strconv"
	"strings"
)

func abs(v int64) int64 {
	if v < 0 {
		return -v
	}
	return v
}
func min(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}
func main() {
	scanner := makeWordScanner()
	x := eGetInt64(scanner)
	k := eGetInt64(scanner)
	d := eGetInt64(scanner)
	var m int64
	x = abs(x)
	if d*k <= x {
		m = x - d*k
	} else {
		cnt := x / d
		k -= cnt
		if k <= 0 {
			m = x - d*k
		} else if k%2 == 0 {
			m = x % d
		} else {
			m = abs((x % d) - d)
		}
	}

	// if x >= 0 {
	// 	for x >= 0 && k > 0 {
	// 		x -= d
	// 		d * k
	// 	}
	// 	if k%2 == 0 {
	// 		m = abs(x)
	// 	} else {
	// 		m = abs(x + d)
	// 	}
	// } else {
	// 	for x <= 0 && k > 0 {
	// 		x += d
	// 		k--
	// 	}
	// 	if k%2 == 0 {
	// 		m = abs(x)
	// 	} else {
	// 		m = abs(x - d)
	// 	}
	// }
	fmt.Println(m)
}

////////////////////////////////////////////////////////////////////////////////
// ライブラリ
////////////////////////////////////////////////////////////////////////////////
const (
	TooLarge = math.MaxInt64
	TooSmall = math.MinInt64
)

func makeScanner(maxByte int) *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Buffer(make([]uint8, 0, 8192), maxByte)
	return scanner
}
func makeCharScanner() *bufio.Scanner {
	scanner := makeScanner(8192)
	scanner.Split(bufio.ScanRunes)
	return scanner
}
func makeWordScanner() *bufio.Scanner {
	scanner := makeScanner(8192)
	scanner.Split(bufio.ScanWords)
	return scanner
}
func eGetLine(r *bufio.Scanner) string {
	if r.Scan() {
		return r.Text()
	}
	err := r.Err()
	if err != nil {
		log.Fatal(err)
	}
	// EOF
	return ""
}
func eGetInt(r *bufio.Scanner) int {
	line := eGetLine(r)
	return eAtoi(line)
}
func eGetInt64(r *bufio.Scanner) int64 {
	line := eGetLine(r)
	return eAtoInt64(line)
}
func eGetFields(r *bufio.Scanner) []string {
	line := eGetLine(r)
	return strings.Fields(line)
}
func eGetInts(r *bufio.Scanner) []int {
	fields := eGetFields(r)
	ints := make([]int, len(fields))
	for i := 0; i < len(ints); i++ {
		ints[i] = eAtoi(fields[i])
	}
	return ints
}
func eGetInt64s(r *bufio.Scanner) []int64 {
	fields := eGetFields(r)
	ints := make([]int64, len(fields))
	for i := 0; i < len(ints); i++ {
		ints[i] = eAtoInt64(fields[i])
	}
	return ints
}
func eGetChars(r *bufio.Scanner) []string {
	line := eGetLine(r)
	return strings.Split(line, "")
}
func eAtoi(s string) int {
	n, err := strconv.Atoi(s)
	if err != nil {
		log.Fatal(err)
	}
	return n
}
func eAtoInt64(s string) int64 {
	n, err := strconv.ParseInt(s, 10, 64)
	if err != nil {
		log.Fatal(err)
	}
	return n
}
func pow(a, n int) int {
	if n == 0 {
		return 1
	}
	if n == 1 {
		return a
	}
	if n%2 == 1 {
		return pow((a*a), n/2) * a
	}
	return pow((a * a), n/2)
}
func pow5(a int, memo map[int]int) int {
	v, ok := memo[a]
	if ok {
		return v
	}

	b := a * a
	c := b * b
	memo[a] = c * 5
	return memo[a]
}
func powMod(a, n, mod int) int {
	if n == 0 {
		return 1 % mod
	}
	if n == 1 {
		return a % mod
	}
	if n%2 == 1 {
		return powMod((a*a)%mod, n/2, mod) * a % mod
	}
	return powMod((a*a)%mod, n/2, mod)
}

func factoricalMod(n, count, mod int) int {
	if count == 1 {
		return n % mod
	}
	return (n % mod) * (factoricalMod(n-1, count-1, mod)) % mod
}

func combinationMod(n, a, mod int) int {
	x := factoricalMod(n, a, mod)
	y := factoricalMod(a, a, mod)
	y = powMod(y, mod-2, mod)
	return ((x % mod) * (y % mod)) % mod
}
func countBitOfOn(i, numbits int) int {
	count := 0
	var bit uint64
	for bit = 0; bit < uint64(numbits); bit++ {
		t := 1 << bit
		if i&t > 0 {
			count++
		}
	}
	return count
}

type ints []int

func ToString(slice []int) string {
	format := fmt.Sprint(slice)
	return fmt.Sprint(format[1 : len(format)-1])
}

type String string

func reverseS(s []int) {
	for i := 0; i < len(s)/2; i++ {
		s[i], s[len(s)-1-i] = s[len(s)-1-i], s[i]
	}
}
func reverseB(s []byte) {
	for i := 0; i < len(s)/2; i++ {
		s[i], s[len(s)-1-i] = s[len(s)-1-i], s[i]
	}
}

func (s String) revese() string {
	b := []byte(s)
	for i := 0; i < len(b)/2; i++ {
		b[i], b[len(b)-1-i] = b[len(b)-1-i], b[i]
	}
	return string(b)
}
func contains(n int, slice []int) bool {
	for _, e := range slice {
		if e == n {
			return true
		}
	}
	return false
}
func rPool(p int, n []int, c []int, cc [][]int) [][]int {
	if len(n) == 0 || p <= 0 {
		return cc
	}
	p--
	for i := range n {
		r := make([]int, len(c)+1)
		copy(r, c)
		r[len(r)-1] = n[i]
		if p == 0 {
			cc = append(cc, r)
		}
		cc = rPool(p, n[i+1:], r, cc)
	}
	return cc
}

func Pool(p int, n []int) [][]int {
	return rPool(p, n, nil, nil)
}