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<iostream>
#include<bits/stdc++.h>

using namespace std;

int main(){
    #ifndef ONLINE_JUDGE
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif
    long long x,k,d;
    cin >> x >> k >> d;
    if(x>0){
        int steps = abs(x)/d;
        int mind = x - (x/d)*d;
        if(abs(mind - d) < mind){
            mind = abs(mind-d);
            steps += 1;
        }
        if(k<steps){
            cout << abs(x - k*d);
        } 
        else{
            if((k-steps)%2) cout << min(abs(mind+d), abs(mind-d));
            else cout << mind;
        }
    }
    else{
        int steps = abs(x)/d;
        int mind = x - (x/d)*d;
        if(abs(mind+d)<mind){
            mind = abs(mind+d);
            steps += 1;
        }
        if(k<steps) cout << abs(x+k*d);
        else{
            if((k-steps)%2) cout << min(abs(mind+d), abs(mind-d));
            else cout << mind;
        }
    }
    return 0;
}