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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
#include "bits/stdc++.h"
using namespace std;

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	
	long long x, k, d;
	cin >> x >> k >> d;
	
	if (abs(x)/d >= k) cout << abs(x) - k*d;
	else {
		int y = k - abs(x)/d;
		cout << (y&1 ? d - abs(x)%d : abs(x)%d);
	}
}