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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.math.BigDecimal;
import java.util.Scanner;

public class Main {

	public static String Y = "Yes";
	public static String N = "No";
	public static long MOD = (long) (Math.pow(10, 9) + 7);
	public static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {

		long x = nl(); //今の座標
		long k = nl(); //移動回数
		long d = nl(); //1回の移動距離

		// out(100000000000043560l * 100l);

		// ひたすら0の近くに行けば良いパターン
		long xAbs = Math.abs(x);

		BigDecimal bk = BigDecimal.valueOf(k);
		BigDecimal bd = BigDecimal.valueOf(d);
		BigDecimal bx = BigDecimal.valueOf(xAbs);

		//out(bk.multiply(bd));

		int res = bk.multiply(bd).compareTo(bx);

		//out(bk.multiply(bd));
		if (res <= 0) {
			out(xAbs - k * d);
		} else {
			// そうでないパターン
			long toriaezukai1 = xAbs / d;
			long toriaezukai2 = (xAbs / d) + 1;
			long now1 = Math.abs(xAbs - toriaezukai1 * d);
			long now2 = Math.abs(xAbs - toriaezukai2 * d);

			//debug("now1 " + now1);
			//debug("now2 " + now2);

			long now = Math.min(now1, now2);

			//debug("now " + now);
			long nokori = 0;
			if (now1 < now2) {
				nokori = k - toriaezukai1;
			} else {
				nokori = k - toriaezukai2;
			}
			// debug("nokori " + nokori);

			if (nokori % 2l == 0) {
				out(now);
			} else {
				out(Math.abs(now - d));
			}
		}

	}

	/*
	 * 以下メソッド集
	 */

	public static void permutation(String q, String ans) {
		// Base Case
		if (q.length() <= 1) {
			System.out.println(ans + q);
		}
		// General Case
		else {
			for (int i = 0; i < q.length(); i++) {
				permutation(q.substring(0, i) + q.substring(i + 1),
						ans + q.charAt(i));
			}
		}
	}

	static char[][] same(char[][] c, int h, int w) {

		char[][] a = new char[h][w];
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				a[i][j] = c[i][j];
			}
		}
		return a;

	}

	static int countkuro(char[][] c) {

		int count = 0;
		for (char[] cc : c) {
			for (char ccc : cc) {
				if ('#' == ccc) {
					count++;
				}
			}
		}
		return count;
	}

	static void debug() {

		out("---");
	}

	static void debug(Object a) {

		out("-------");
		out(a);
		out("-------");
	}

	static int ketasuu(int n) {

		String str = "" + n;
		return str.length();
	}

	static int account(String str) {

		String target = "AC";
		int count = 0;
		int len = str.length();
		for (int i = 0; i < len - 1; i++) {
			if (target.equals(str.substring(i, i + target.length()))) {
				count++;
			}
		}
		return count;
	}

	static int ni() {

		return sc.nextInt();
	}

	static long nl() {

		return sc.nextLong();
	}

	static double nd() {

		return sc.nextDouble();
	}

	static String n() {

		return sc.next();
	}

	static char[] nc() {

		return sc.next().toCharArray();
	}

	static int kaijo(int n) {

		if (n == 0 || n == 1) {
			return 1;
		} else {
			return n * kaijo(n - 1);
		}
	}

	static int fib(int n) {

		return (n == 1 || n == 0) ? n : fib(n - 2) + fib(n - 1);
	}

	static long lcm(long m, long n) {

		return m * n / gcd(m, n);
	}

	static int lcm(int m, int n) {

		return m * n / gcd(m, n);
	}

	static long gcd(long a, long b) {

		return (b == 0) ? a : gcd(b, a % b);
	}

	static int gcd(int a, int b) {

		return (b == 0) ? a : gcd(b, a % b);
	}

	static void out(Object obj) {
		System.out.println(obj);
	}

	static void outn(Object obj) {
		System.out.print(obj);
	}

	static double max(double d, double e) {

		return Math.max(d, e);
	}

	static long max(long a, long b) {

		return Math.max(a, b);
	}

	static long min(long d, long e) {

		return Math.min(d, e);
	}

	static int min(int a, int b) {

		return Math.min(a, b);
	}
}

class XY {

	int h;
	int c;

	XY(int h, int c) {
		this.h = h;
		this.c = c;
	}
}