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: Runtime Error)

#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#endif

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll solve(ll x, ll k, ll d){
	x = abs(x);

	/*if (k == 0){
		return x;
	}*/

	if (k % 2 == 1){
		return min(solve(x-d, k-1, d),
               solve(x+d, k-1, d));
	}

	d *= 2;
	k /= 2;

	if (x/k >= d){
		return x - d*k;
	}

	x %= d;
	return min(x, d-x);
}

int main(){
	std::ios::sync_with_stdio(false);
	ll x, k, d;
	cin >> x >> k >> d;
	cout << solve(x, k, d) << endl;
	return 0;
}