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.math.BigInteger;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc = new Scanner(System.in);
		BigInteger x = new BigInteger(sc.next());
		BigInteger k = new BigInteger(sc.next());
		BigInteger d = new BigInteger(sc.next());
		BigInteger abs = x.abs();
		BigInteger goal = null;
		
		BigInteger div = abs.divide(d);
		if (div.compareTo(k) > 0) {
			goal = abs.subtract(d.multiply(k));
		} else if (div.compareTo(k) == 0) {
			goal = abs.subtract(d.multiply(k));
		} else {
			// 距離縮める
			abs = abs.subtract(d.multiply(div));
			// 残り試行が奇数か偶数か
			BigInteger exa = k.subtract(div).mod(BigInteger.TWO);
			if (exa.equals(BigInteger.ZERO)) {
				// 偶数回
				goal = abs;
			} else {
				goal = abs.subtract(d).abs();
			}
		}
		System.out.println(goal);
	}
}
