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 a,b,c;
	cin>>a>>b>>c;
	a=abs(a);
if(a>0&&a/c>=b)
cout<<a-b*c<<endl;
else
{
long long int f=a/c;
a-=f*c;
b-=f;
if(b%2==0)
cout<<abs(a)<<endl;
else
cout<<min(abs(a+c),abs(a-c))<<endl;;
}
	return 0;
}
