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: Accepted)

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include<unistd.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
#define ST first
#define ND second
#define ll long long
#define ld long double
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
using namespace std;
using namespace __gnu_pbds;

// replace ll  with pair if multiset needed
typedef tree<pair<ll,ll>, null_type, greater<pair<ll,ll> >, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
ordered_set secik;

const ll  INF = 1e9 + 9;
const ll  MOD = 1e9 + 7;
const long long LINF = (ll)1e18 + 3;

// secik.insert({x, t++});
// secik.erase(secik.lower_bound({x,-1}));
// *secik.find_by_order(x)).first << "\n";
// secik.order_of_key(x)

//random_device device;
//mt19937 gener(device());
//uniform_int_distribution<ll > gen(0,n-1);
//gen(gener); // generate random number

int main(){
	ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);

	ll x,k,d; cin >> x >> k >> d;
	
	if(abs(x) / d > k){
		cout << abs(x) - k * d;
	} else {
		if((k - abs(x) / d) % 2 == 0) cout << abs(x) % d;
		else cout << d - abs(x) % d;
	}
	
	return 0;
}