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++ (Clang 10.0.0) (judge verdict: Accepted)

#include<functional>
#include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<utility>
#include<string>
#include<cstdio>
#include<vector>
#include<bitset>
#include<cmath>
#include<ctime>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
using namespace std;
const int inf=2147483647,dx[]={-1,0,1,0},dy[]={0,-1,0,1};// 上 左 下 右
const int N=100005,M=1000005,K=200005,mod=1000000007;
const long long llinf=9223372036854775807ll;
//int & long long
long long x,k,d,k2,l;
int main(){
	cin>>x>>k>>d;
	k2=abs(x)/d;
	if(k2>k)
	{
		if(x>0)
			cout<<x-k*d;
		else
			cout<<abs(x+k*d);
	}
	else
	{ 
		if(x>0)
			l=x-k2*d;
		else
			l=abs(x+k2*d);
		k-=k2;
		if(k%2==0ll)
			cout<<l;
		else
			cout<<abs(l-d);
	}
	return 0;
}