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 <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <tuple>
#include <cstdint>
#include <cstdio>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <cctype>
#include <numeric>
#include <cmath>

#define ll long long int
#define pb push_back
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
using namespace std;

int mx8[] = {0,0,1,-1,-1,1,-1,1};
int my8[] = {-1,1,0,0,-1,-1,1,1};
int mx4[] = {1,-1,0,0};
int my4[] = {0,0,-1,1};
const int MOD = 1000000007;


int main(){
    ll x, k, d;
    cin >> x >> k >> d;
    x = abs(x);

    ll s = x / d;
    if(s >= k){cout << x - d * k << endl; return 0;}

    ll MIN_right = x - d * s;
    ll MIN = min(MIN_right,d-MIN_right);

    if(MIN==MIN_right){
        if((k-s)%2==0){
            cout << MIN_right << endl;
        }else{
            cout << d - MIN << endl;
        }
    }else{
        if((k-s)%2==0){
            cout << MIN << endl;
        }else{
            cout << MIN_right << endl;
        }
    }
}