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>
#define LL long long
LL myabs(LL a){
	return a>=0?a:-a;
}
int main(){
	LL x,k,d,ans;
	scanf("%lld%lld%lld",&x,&k,&d);
	x=myabs(x);
	if(x/d>=k)ans=x-k*d;
	else{//x/d<k
		k-=x/d;
		if(k%2==0)ans=x%d;
		else ans=d-x%d;
	}
	printf("%lld\n",ans);
	return 0;
}