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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner(System.in);
		long x = sc.nextLong(), k = sc.nextLong(), d = sc.nextLong();
		x = Math.abs(x);
		long min1 = x%d, min2 = Math.abs(min1-k);
		long mov1 = x/d, mov2 = mov1 + 1;
/*		if(min1 != 0) {
			mov1++;
			mov2++;
		}*/
		long ans = 0;
		if(k < mov1) {
			ans = x - k*d;
		}else {
			if(k == min1) {
				ans = min1;
			}else if(k == min2) {
				ans = min2;
			}else{
				long c1 = k - mov1, c2 = k - mov2;
				if(c1%2 == 0) {
					ans = min1;
				}else {
					ans = min2;
				}
			}
		}
		System.out.println(ans);
	}

	static class FastScanner {
		private BufferedReader reader = null;
	    private StringTokenizer tokenizer = null;
	    public FastScanner(InputStream in) {
	        reader = new BufferedReader(new InputStreamReader(in));
	        tokenizer = null;
	    }

	    public String next() {
	        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
	            try {
	                tokenizer = new StringTokenizer(reader.readLine());
	            } catch (IOException e) {
	                throw new RuntimeException(e);
	            }
	        }
	        return tokenizer.nextToken();
	    }

	    public String nextLine() {
	        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
	            try {
	                return reader.readLine();
	            } catch (IOException e) {
	                throw new RuntimeException(e);
	            }
	        }

	        return tokenizer.nextToken("\n");
	    }

	    public long nextLong() {
	        return Long.parseLong(next());
	    }

	    public int nextInt() {
	        return Integer.parseInt(next());
	    }

	    public double nextDouble() {
	         return Double.parseDouble(next());
	     }

	    public int[] nextIntArray(int n) {
	        int[] a = new int[n];
	        for (int i = 0; i < n; i++)
	            a[i] = nextInt();
	        return a;
	    }

	    public long[] nextLongArray(int n) {
	        long[] a = new long[n];
	        for (int i = 0; i < n; i++)
	            a[i] = nextLong();
	        return a;
	    }
	}
}