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
//package abc175;

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] ip = br.readLine().split(" ");
		
		long X = Long.parseLong(ip[0]);
		long K = Long.parseLong(ip[1]);
		long D = Long.parseLong(ip[2]);
		
		long ans = 0;
		
		if(X > 0) {
			long tmp_k = Math.min(K, Math.abs(X)/D + 1);
			K -= tmp_k;
			X -= tmp_k*D;
		}else {
			long tmp_k = Math.min(K, Math.abs(X)/D + 1);
			K -= tmp_k;
			X += tmp_k*D;
		}
		ans = Math.abs(X);
		if(K > 0) {
			if(K%2 == 1) {
				if(X > 0) {
					ans = Math.abs(X-D);
				}else {
					ans = Math.abs(X+D);
				}
			}
		}
		
		System.out.println(ans);
	}
	
}
