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>
#define ll long long int
using namespace std;
int main()
{
    ll a,b,c,n,m,r,d;
    cin>>a>>b>>c;
    a=abs(a);
    if(a/c>=b)
        cout<<a-b*c<<endl;
    else{
        b-=a/c;
        if(b%2==0)cout<<a%c<<endl;
        else cout<<c-(a%c)<<endl;
    }

}
