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>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;
using ll=long long;

int main()
{
  ll x, k, d;
  cin >> x >> k >> d;
  
  int isPlus;
  ll cnt = 0;
  ll ans = 0;
  
  bool isEven;
  bool isOver;
  
  int korn = k;
  
  //xを正で考える。
  if(x > 0) isPlus = 1;
  else
  { 
    x *= -1;
    isPlus = -1;
  }
  
  cnt = x / d;
  
  if(x % d < -x%d+d)
  {
    k -= cnt;
    isOver = false;
  }
  else
  {
    k -= (cnt+1);
    isOver = true;
  }
  
  if(k < 0)
  {
    cout << abs(isPlus * (x-d*korn));
    return 0;
  }
  
  if(k%2 == 0) isEven = true;
  else isEven = false;
  
  if(isOver && isEven) ans = isPlus*(x - (cnt+1)*d);
  else if(isOver && !isEven) ans = isPlus*(x-cnt*d);
  else if(!isOver && isEven) ans = isPlus*(x-cnt*d);
  else ans = isPlus * (x-(cnt+1)*d);
  
  cout << abs(ans);  
  
  return 0;
}