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>
#define maxn 
using namespace std;

int main() {
	long long X, K, D;
	cin >> X >> K >> D;
	if(X < 0) X = -X;
	long long d = X / D;
	if(d > K) {
		X -= K * D;
	} else {
		if((K - d) & 1) X = D - X % D;
		else X %= D;
	}
	cout << X;
	return 0;
}