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Contest: Task: Related: TaskB TaskD

Score : $300$ points

Problem Statement

You are given an integer $X$. The following action on this integer is called an operation.

Choose and do one of the following.
- Add $1$ to $X$.
- Subtract $1$ from $X$.

The terms in the arithmetic progression $S$ with $N$ terms whose initial term is $A$ and whose common difference is $D$ are called good numbers.
Consider performing zero or more operations to make $X$ a good number. Find the minimum number of operations required to do so.

Constraints

All values in input are integers.
$-10^{18} \le X,A \le 10^{18}$
$-10^6 \le D \le 10^6$
$1 \le N \le 10^{12}$

Input

Input is given from Standard Input in the following format:

$X$ $A$ $D$ $N$

Output

Print the answer as an integer.

Sample Input 1

6 2 3 3

Sample Output 1

Since $A=2,D=3,N=3$, we have $S=(2,5,8)$.
You can subtract $1$ from $X$ once to make $X=6$ a good number.
It is impossible to make $X$ good in zero operations.

Sample Input 2

0 0 0 1

Sample Output 2

We might have $D=0$. Additionally, no operation might be required.

Sample Input 3

998244353 -10 -20 30

Sample Output 3

998244363

Sample Input 4

-555555555555555555 -1000000000000000000 1000000 1000000000000