#include <bits/stdc++.h>
using namespace std;
int main()
{
 long long i,j,k,a,b,c=0,n,x,y,d;
 cin>>x>>k>>d;
 x=abs(x);
 y=x/d;
 if(y>=k) cout<<x-(k*d)<<endl;
 else
 {
   k=k-y;
   if(k%2==0) cout<<x-(y*d)<<endl;
   else cout<<abs(x-(y+1)*d)<<endl;
 }
return 0;
}

### Prompt

Please formulate 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>
using namespace std;
int main()
{
 long long i,j,k,a,b,c=0,n,x,y,d;
 cin>>x>>k>>d;
 x=abs(x);
 y=x/d;
 if(y>=k) cout<<x-(k*d)<<endl;
 else
 {
   k=k-y;
   if(k%2==0) cout<<x-(y*d)<<endl;
   else cout<<abs(x-(y+1)*d)<<endl;
 }
return 0;
}

```