#include<bits/stdc++.h>
using namespace std;

int main(){
    long long x,k,d;
    scanf("%lld %lld %lld",&x,&k,&d);
    x=abs(x);
    if (x/d>k) {
        printf("%lld\n",x%d+d*(x/d-k));
    } else {
        printf("%lld\n",(k-x/d)%2==0?x%d:abs(x%d-d));
    }
    return 0;
}

### Prompt

Please create a solution in Cpp 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 x,k,d;
    scanf("%lld %lld %lld",&x,&k,&d);
    x=abs(x);
    if (x/d>k) {
        printf("%lld\n",x%d+d*(x/d-k));
    } else {
        printf("%lld\n",(k-x/d)%2==0?x%d:abs(x%d-d));
    }
    return 0;
}

```