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<bits/stdc++.h>
using namespace std;
int main()
{
   long long int x,d, k;
   cin>>x>>k>>d;
   x=abs(x);
   long long int steps=k-min(k, x/d);
       x-=(min(k, (x/d))*d);
       k=steps;
       if(k%2==0) cout<<abs(x)<<endl;
       else cout<<abs(x-d)<<endl;
} 
