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;

long long x, k, d;

int main() {
	scanf("%lld%lld%lld", &x, &k, &d);
	x = abs(x);
	long long tmp = min(k, x / d);
	x -= tmp * d;
	k -= tmp;
	tmp = abs(x - d);
	printf("%lld\n", k % 2 == 0 ? x : tmp);
}