Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long int
#define int long long
#define f(i,l,n) for(int i=l;i<n;i++) 
#define E "\n"

int solve()
{
	return 0;	
}


int32_t main()
{

   
  long double n,k,d;
  cin >> n >> k >> d;

  if(k*d<abs(n))
  {

  	cout<<fixed<<setprecision(18)<<(int)(abs(n)-k*d)<<E;
  	return 0;
  }

  n=abs(n);
  if(d>=n)
  {
  	if(d==n) cout<<fixed<<setprecision(18)<<(int)n<<E;
  	else cout<<fixed<<setprecision(18)<<(int)min(n,d-n)<<E;
  	return 0;
  }
  int dif=k*d-n,D=d;
  int dis=d-dif%D;
  cout<<fixed<<setprecision(18)<<dis<<E;
  
  
 


     return 0;
    
}