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 X,K,D,answer,amari;
	scanf("%lld",&X);
	scanf("%lld",&K);
	scanf("%lld",&D);
	if(X<0)X=-1*X;
	if(X/D>K)answer=X-D*K;
	else{
		amari=X%D;
		K-=X/D;
		if(K%2!=0)answer=D-amari;
		else answer=amari;
	}
	printf("%lld",answer);
	return 0;
}