Problem7990--ABC255 —— C - ±1 Operation 1

7990: ABC255 —— C - ±1 Operation 1

[Creator : ]
Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

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.

Input

Input is given from Standard Input in the following format:
$X\ A\ D\ N$

Output

Print the answer as an integer.

Constraints

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

Sample 1 Input

6 2 3 3

Sample 1 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 2 Input

0 0 0 1

Sample 2 Output

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

Sample 3 Input

998244353 -10 -20 30

Sample 3 Output

998244363

-555555555555555555 -1000000000000000000 1000000 1000000000000

444445

Source/Category