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>
int main(void)
{
	long long a,b,c,d,e,f,g;
	scanf("%lld %lld %lld",&a,&b,&c);
	if(a<0) a=-a;
	d=a/c;
	e=a%c;
	if(d<=b){
		f=d-b;
		if(f%2==0){
			printf("%lld\n",e);
		}
		else {
			printf("%lld\n",c-e);
		}
	}
	else {
		printf("%lld\n",a-(b*c));
	}
	return 0;
}
