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
#include <stdio.h>
typedef long long LL;

int main()
{	 
	LL x, k, d, y, z;
	
	scanf("%lld%lld%lld", &x, &k, &d);	
	if(x < 0) x = -x;
	y = x / d;
	if(y >= k) z = x - d * k;
	else{
		z = x % d;
		if((k - y) & 1) z = d - z;
	}
	printf("%lld\n", z);
		
	return 0;
}