#include<bits/stdc++.h>
#define ll long long int
using namespace std;
int main(){
ll t;
t=1;
//cin>>t;
while(t--){
ll x,k,d;
cin>>x>>k>>d;
x=abs(x);
ll ki = x/d;
if(ki>k){
    cout<< x - k*d;
}
else
{
    k-=ki;
    if(k&1)
    cout<<d - x%d;
    else
    cout<<x%d<<endl;
}


}

}
### 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 ll long long int
using namespace std;
int main(){
ll t;
t=1;
//cin>>t;
while(t--){
ll x,k,d;
cin>>x>>k>>d;
x=abs(x);
ll ki = x/d;
if(ki>k){
    cout<< x - k*d;
}
else
{
    k-=ki;
    if(k&1)
    cout<<d - x%d;
    else
    cout<<x%d<<endl;
}


}

}
```