#include <bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i=0;i<(n);i++)
typedef long long ll;

int main(){
  ll x,k,d,ans=0;cin>>x>>k>>d;
  if(x<0) x*=-1;
  if(x/d<=k){
    ans=x%d;
    k-=x/d;
    if(k%2)ans=abs(ans-d);
  }else{
    ans=x-d*k;
  }

  cout<<ans;
}


### 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>
using namespace std;
#define REP(i,n) for(int i=0;i<(n);i++)
typedef long long ll;

int main(){
  ll x,k,d,ans=0;cin>>x>>k>>d;
  if(x<0) x*=-1;
  if(x/d<=k){
    ans=x%d;
    k-=x/d;
    if(k%2)ans=abs(ans-d);
  }else{
    ans=x-d*k;
  }

  cout<<ans;
}


```