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 <unistd.h>
using namespace std;
#define nl cout<<"\n"
#define pb push_back
#define se second
#define fi first
#define int long long 
#define pi pair<int,int>
#define vpi vector<pi>
#define vvpi vector<vpi>
#define fio ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL)
#define For(i,n) for(int i=0;i<n;i++)
#define Forn(i,a,n) for(int i=a;i<n;i++)
#define pie =3.14159265358979323846264338327950;
const int mod= 998244353;



void solve(){
	fio;
	int x,k,d;
	cin>>x>>k>>d;
	int div= x/d;
	if(div>=k){
		cout<<x-k*d<<endl;
	}
	else{
		int left= k-div;
		if(left%2) cout<<abs(x-div*d-d)<<endl;
		else cout<<x-div*d<<endl;
	}
}


int32_t main(){
	fio;
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int t=1;
	//cin>>t;
	for(int i=1;i<=t;i++){ 
		//cout<<"Case #"<<i<<":\n";
		solve();
	}
	return 0;
}