#include <bits/stdc++.h>
#define ll long long
using namespace std;
int main()
{
    ll x,k,d,s;
    cin >> x >> k >> d;
    s = (x == 0 ? 1 : x/abs(x));
    ll div = abs(x)/d;
    div = min(div,k);
    k -= div;
    if(k&1) div++;
    cout << abs(abs(x) - div*d) << endl;
}

### Prompt

Your task is to create 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
using namespace std;
int main()
{
    ll x,k,d,s;
    cin >> x >> k >> d;
    s = (x == 0 ? 1 : x/abs(x));
    ll div = abs(x)/d;
    div = min(div,k);
    k -= div;
    if(k&1) div++;
    cout << abs(abs(x) - div*d) << endl;
}

```