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 ll long long
using namespace std;
int main(){
    ll x,k,d;
    cin>>x>>k>>d;
    if(k == 0)cout<<abs(x)<<endl;
    else if(x == 0 && k%2 == 0)cout<<0<<endl;
    else if(x == 0 && k%2 == 1)cout<<d<<endl;
    else{
        if(x < 0)
        {
            if(x + k*d < 0)cout<<abs(x + k*d)<<endl;
            else{
            while(abs(x) >= d && k != 0)
            {
                x += d;
                k--;
            }
            if(k == 0)cout<<abs(x)<<endl;
            else{
            if(k%2 == 0)cout<<abs(x)<<endl;
            else{
                cout<<min(abs(x+d),abs(x-d));
            }
            }


            }
        }
        else if(x > 0)
        {
            if(x - k*d < 0)cout<<abs(x - k*d)<<endl;
            else{
            while(abs(x) >= d && k != 0)
            {
                x -= d;
                k--;
            }
            if(k == 0)cout<<abs(x)<<endl;
            else{
            if(k%2 == 0)cout<<abs(x)<<endl;
            else{
                cout<<min(abs(x+d),abs(x-d));
            }
            }
            }
        }
    }
	return 0;
}