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.util.*;
import java.awt.Frame;
import java.io.*;

public class Main {
	// static ArrayList<Integer>[] g;

	static pair[] a;
	static int[][] memo;

	static int dp(int l, int r) {
		if (l > r)
			return 0;
		if (memo[l][r] != -1)
			return memo[l][r];
		int ans = dp(l + 1, r);
		ans = Math.max(ans, dp(l, r - 1));
		for (int idx : startAt[l]) {
			if (a[idx].y >= r)
				continue;
			int inc = exist[a[idx].y + 1][r] ? 1 : 0;
			ans = Math.max(ans, 1 + dp(a[idx].x, a[idx].y) + inc + dp(a[idx].y + 1, r));
		}
		for (int idx : endAt[r]) {
			if (a[idx].x <= l)
				continue;
			int inc = exist[l][a[idx].x - 1] ? 1 : 0;
			ans = Math.max(ans, 1 + dp(a[idx].x, a[idx].y) + inc + dp(a[idx].y + 1, r));
		}

		return memo[l][r] = ans;
	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		long x = Long.parseLong(st.nextToken());
		long k = Long.parseLong(st.nextToken());
		long d = Long.parseLong(st.nextToken());
		long r = Math.abs(0 - x);
		long c = r / d;
		if (x > 0) {
			if (c > k) {
				x -= k * d;
			} else {
				x -= c * d;
				k -= c;
				if (k % 2 == 1)
					x -= d;
			}

		} else {
			if (c > k) {
				x += k * d;
			} else {
				x += c * d;
				k -= c;
				if (k % 2 == 1)
					x += d;
			}
		}
		pw.println(Math.abs(x));
		pw.flush();
		pw.close();

	}

	static int maxSize;
	static boolean[][] exist;
	static ArrayList<Integer>[] startAt, endAt;

	static void compress(pair[] arr) {
		TreeSet<Integer> tr = new TreeSet<>();
		for (int i = 0; i < arr.length; i++) {
			tr.add(arr[i].x);
			tr.add(arr[i].y);
		}
		tr.add(0);
		tr.add((int) 1e9);
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int x : tr)
			hm.put(x, hm.size());
		for (int i = 0; i < arr.length; i++) {
			arr[i].x = hm.get(arr[i].x);
			arr[i].y = hm.get(arr[i].y);
		}
		maxSize = hm.size();
	}

	static class pair implements Comparable<pair> {
		int x;
		int y;

		public pair(int d, int u) {
			x = d;
			y = u;
		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			int x1 = y - x;
			int x2 = o.y - o.x;
			return x1 - x2;
		}

	}

}