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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;

public class Main{

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);
		String[] t = scanner.nextLine().split(" ");
		long x = Math.abs(Long.parseLong(t[0]));
		long k = Long.parseLong(t[1]);
		long d = Long.parseLong(t[2]);
		long ans = 0;

		long sho   = Math.floorDiv(x, d);
		long amari = x - sho * d;

		if(sho > k) {

			ans = x - k * d;
		}else {
			ans = Math.abs(amari - d * (Math.abs(k - sho) % 2));
		}

		System.out.println(ans);
	}
}