#include <stdio.h>
long long x, k, d;
int main() {
	scanf("%lld%lld%lld", &x, &k, &d);
	if (x < 0)x = -x;
	if (x / d >= k) {
		printf("%lld\n", x - d * k);
		return 0;
	}
	if ((x / d + k) % 2) {
		printf("%lld\n", (x / d + 1) * d - x);
	}
	else {
		printf("%lld\n", x - x / d * d);
	}
}
### Prompt

Develop a solution in Cpp to the problem described below:

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

### Response

```cpp
#include <stdio.h>
long long x, k, d;
int main() {
	scanf("%lld%lld%lld", &x, &k, &d);
	if (x < 0)x = -x;
	if (x / d >= k) {
		printf("%lld\n", x - d * k);
		return 0;
	}
	if ((x / d + k) % 2) {
		printf("%lld\n", (x / d + 1) * d - x);
	}
	else {
		printf("%lld\n", x - x / d * d);
	}
}
```