Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

/*      Welcome to my Code      */

#include <bits/stdc++.h>
#define ll                      long long int
#define i(a,n)                  int a=n;
#define l(a,n)                  ll a=n;
#define d(a,n)                  double a=n;
#define s(a)                    string a;
#define c(a)                    ll a; cin>>a;a
#define cd(a)                   double a; cin>>a;
#define cs(a)                   string a; cin>>a;
#define ci(a)                   cin>>a;
#define co(a)                   cout<<a;
#define cos(a)                  cout<<a<<" "
#define con(a)                  cout<<a<<endl
#define yes                     cout<<"YES"<<endl
#define no                      cout<<"NO"<<endl
#define nl                      cout<<endl
#define ca(arr,n)               for(ll i=0;i<n;i++) cin>>arr[i]
#define caa(arr,n)              c(n); ll arr[n]; for(ll i=0;i<n;i++) cin>>arr[i];
#define f0(i,a,n)               for(ll i=a;i>=n;i--)
#define f(i,n)                  for(ll i=0;i<n;i++)
#define f1(i,a,n)               for(ll i=a;i<n;i++)
#define lcm(a,b)                (a*b)/__gcd(a,b)
#define T                       ll t=1; cin>>t; while(t--)
#define fast                    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define ret(x)                  return cout<<x,0;

using namespace std;

int main()
{
    fast;
    c(x);c(k);c(d);
    x=abs(x);
    if(x/d>=k) con(x-(k*d));
    else
    {
        k=k-x/d;
        if(k%2==0) con(abs(x%d-d));
        else con(x%d);
    }
    return 0;
}

/*It's not who I am underneath, but what I do that defines me

MMMMMMMMMMMMMMMMMMMMM.                             MMMMMMMMMMMMMMMMMMMMM
 `MMMMMMMMMMMMMMMMMMMM           M\  /M           MMMMMMMMMMMMMMMMMMMM'
   `MMMMMMMMMMMMMMMMMMM          MMMMMM          MMMMMMMMMMMMMMMMMMM'
     MMMMMMMMMMMMMMMMMMM-_______MMMMMMMM_______-MMMMMMMMMMMMMMMMMMM
      MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
      MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
      MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
     .MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM.
    MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
                   `MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM'
                          `MMMMMMMMMMMMMMMMMM'
                              `MMMMMMMMMM'
                                 MMMMMM
                                  MMMM
                                   MM
*/