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"
	"os"
	"sort"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

type st struct {
	ind int
	min int64
}

func main() {
	var X int64
	var K int64
	var D int64
	fmt.Scan(&X)
	fmt.Scan(&K)
	fmt.Scan(&D)
	max := X + K*D
	min := X - K*D
	if X/D < -K {
		fmt.Println(-max)
		return
	}
	if X/D > K {
		fmt.Println(min)
		return
	}
	if X > 0 {
		y := X % (2 * D)
		if y >= D {
			fmt.Println(2*D - y)
			return
		} else {
			fmt.Println(y)
			return
		}
	} else {
		y := -X % (2 * D)
		if y >= D {
			fmt.Println(2*D - y)
			return
		} else {
			fmt.Println(y)
			return
		}
	}
	// sc.Split(bufio.ScanWords)

}
func bc(s string, pos int) string {
	ch := "1"
	if string(s[pos]) == "1" {
		ch = "0"
	}
	pre := string(s[:pos])
	post := ""
	if pos != len(s)-1 {
		post = string(s[pos+1:])
	}
	tmp := pre + ch + post
	return tmp
}
func popCount(n string) int {
	count := 0
	for _, s := range n {
		if string(s) == "1" {
			count++
		}
	}
	return count
}
func chc(m [][]bool, p int) [][]bool {
	ret := make([][]bool, len(m))
	for i, l := range m {
		tmp := []bool{}
		for _, c := range l {
			if i == p {
				tmp = append(tmp, false)
			} else if c == true {
				tmp = append(tmp, true)
			} else {
				tmp = append(tmp, false)
			}
		}
		ret[i] = tmp
	}
	return ret
}
func chl(m [][]bool, p int) [][]bool {
	ret := make([][]bool, len(m))
	for j, l := range m {
		tmp := []bool{}
		for i, c := range l {
			if i == p {
				tmp = append(tmp, false)
			} else if c == true {
				tmp = append(tmp, true)
			} else {
				tmp = append(tmp, false)
			}
		}
		ret[j] = tmp
	}
	return ret
}
func helper(ma [][]bool) int {
	count := 0
	for _, l := range ma {
		for _, c := range l {
			if c == true {
				count++
			}
		}
	}
	return count
}
func nextLine() string {
	sc.Scan()
	return sc.Text()
}
func nextInt() int64 {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return int64(i)
}
func MySort(a []int) {
	sort.Slice(a, func(i, j int) bool { return a[i] < a[j] })

}
func SortedBinaryAppend(sortedArr []int, targetValue int) []int {
	return []int{}
}
func SortedBinaryDelete(sortedArr []int, targetValue int) []int {
	return []int{}
}
func SortedBinarySearch(sortedArr []int, targetValue int) int {
	post := len(sortedArr) - 1
	pre := 0
	for {
		div := (post + pre) / 2
		tim := sortedArr[div]
		if tim == targetValue {
			return pre + div
		} else if tim > targetValue {
			post = tim
		} else {
			pre = tim
		}
		if pre == post {
			return -1
		}
	}
}
func Abs(i int) int {
	if i < 0 {
		return -1 * i
	}
	return i
}
func Min(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func Max(a, b int) int {
	if a > b {
		return a
	}
	return b
}
func CalcNum(tate int, yoko int, A int, B int, dp *map[[2]int]int) int {
	if (*dp)[[2]int{tate, yoko}] != 0 {
		return (*dp)[[2]int{tate, yoko}]
	}
	return yoko*CalcNum(tate-1, yoko, A, B, dp) + tate*CalcNum(tate, yoko-1, A, B, dp)
}
func arrSum(arr []int) int {
	sum := 0
	for _, a := range arr {
		sum += a
	}
	return sum
}
func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Scan(&num)
		nums = append(nums, num)
	}
	return
}
func scanStrings(len int) (strings []string) {
	var str string
	for i := 0; i < len; i++ {
		fmt.Scanf("%s", &str)
		strings = append(strings, str)
	}
	return
}