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<cstdio>
#include<algorithm>
using namespace std;
long long a,b,c,x,y;
int main(){
    scanf("%lld%lld%lld",&a,&b,&c);
    if(a<0)a*=-1;
    x=a/c;
    if(x>=b)printf("%lld",a-b*c);
    else{
        y=a-x*c;
        b=(b-x)&1;
        printf("%lld",abs(y-c*(b?1:0)));
    }
}
