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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
#include<bits/stdc++.h>

using namespace std;
#define int long long
const int N = 6666;
int x,k,d;
signed main(){
	cin>>x>>k>>d;
	if(x<0) x*=-1;
	int tmp=x/d;
	int ans=0;
	if(tmp>=k) ans=x-k*d;
	else{
		ans=x-d*tmp;
		k-=tmp;
		if(k%2) ans=abs(ans-d);
		
	}
	cout<<ans;
	return 0;
}