#include<bits/stdc++.h>
#define int long long
using namespace std;
int x,k,d,a,b;
signed main()
{
	scanf("%lld %lld %lld",&x,&k,&d);
	x=abs(x);
	a=x/d;
	b=x%d;
	if(k<=a)
		cout<<x-k*d<<endl;
	else
	{
		a-=k;
		if(a&1)
			cout<<d-b<<endl;
		else
			cout<<b<<endl;
	}
	return 0;
} 
### Prompt

Your challenge is to write a Cpp solution to the following problem:

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<bits/stdc++.h>
#define int long long
using namespace std;
int x,k,d,a,b;
signed main()
{
	scanf("%lld %lld %lld",&x,&k,&d);
	x=abs(x);
	a=x/d;
	b=x%d;
	if(k<=a)
		cout<<x-k*d<<endl;
	else
	{
		a-=k;
		if(a&1)
			cout<<d-b<<endl;
		else
			cout<<b<<endl;
	}
	return 0;
} 
```