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.

6 2 3 3

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.

0 0 0 1

0

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

998244353 -10 -20 30

998244363

-555555555555555555 -1000000000000000000 1000000 1000000000000

444445