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 REP(i, n) for(int i=0; i<(int)(n); i++)
int main(){
long X, K, D, ans=0; cin >> X >> K >> D;
long Y=abs(X), k=Y/D;
if(K<=k){ ans=Y-K*D; }
else{ 
  Y=Y-k*D; K=K-k; 
  ans=(K%2)?abs(Y-D):Y;
}
cout << ans << "\n";
}