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.Scanner;

public class Main {
	static long solve(long X , long K , long D){
		if(X >= 0){
			long ret = X;
			if(X / D >= K){
				return ret - K * D;
			}
			// X < K * D
			long k = X / D;
			ret = X - k * D;
			K -= k;
			if(K % 2 == 0){
				return ret;
			}else{
				return Math.abs(ret - D);
			}
		}else{
			return solve(- X , K , D);
		}
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long X = sc.nextLong();
		long K = sc.nextLong();
		long D = sc.nextLong();
		long r = solve(X , K , D);
		
		System.out.println(r);
	}

}
