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)

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define mod ((int)1e9+7)
#define lim 1000000000000000007
#define lim1 18446744073709551615  //Unsigned
#define sq(a) ((a)*(a))
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define mms(v,i) memset(v,i,sizeof(v))
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define REP(i,a,b) for (int i = a; i <= b; i++)
#define REPN(i,a,b) for (int i = a; i >= b; i--)
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef pair<int,int> pi;
typedef pair<ll,ll> PL;
typedef pair<ll,int> PLI;
typedef pair<int,ll> PIL;
typedef pair<int,pair<int,int> > pii;
typedef pair<double,double> pdd;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;
typedef tree<pi,null_type,less<pi>,rb_tree_tag,tree_order_statistics_node_update> indexed_set_pair;
ll power(ll a,ll b) {
   ll res=1;
   while(b){
      if(b%2==1) res=(res*a)%mod;
      a=(a*a)%mod;
      b>>=1;
   }
   return res;
}
ll gcdll(ll a,ll b) {
    if (b==0) return a;
    return gcdll(b,a%b);
}
int gcd(int a,int b) {
    if (b==0) return a;
    return gcd(b,a%b);
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

const int N = (int)2e5+5;
const int M = (int)1e3+5;
const int Q = 102;
const int logN = 19;

const double pie = acos(-1);

void check(ll& ans, ll p, ll x, ll k, ll d) {
  if(abs(p)<=k && (abs(p))%2 == k%2) {
    ll pos = x - p * d;
    ans = min(ans, (ll)abs(pos));
  }
}
void solve() {
  ll x,k,d;
  cin>>x>>k>>d;
  if(x<0) x = -x;
  ll p = x/d;
  ll ans = lim;
  REP(i,-5,5) {
    check(ans, p+i, x, k, d);
  }
  cout<<ans;
}

int main() {
    //freopen("./sort/b2.in","r",stdin);
    //freopen("output.txt","w",stdout);

    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int T=1;
    //cin>>T;
    REP(TC,1,T) {
        //cout<<"Case #"<<TC<<": ";
        solve();
        //cout<<"\n";
    }
}