Score : $300$ points

问题描述

给定一个整数 $X$。以下对该整数的操作被称为 操作。

• 选择并执行以下任一操作：
  • 将 $1$ 加到 $X$ 上。
  • 从 $X$ 中减去 $1$。

在等差数列 $S$ 中，具有 $N$ 项且首项为 $A$、公差为 $D$ 的各项被称为 好数。

考虑通过执行零次或多次操作，使 $X$ 变成一个好数。找出完成这一目标所需的最少操作次数。

以上为通义千问 qwen-max 翻译，仅供参考。

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

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

0

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

Sample Output 4

444445

update @ 2024/3/10 10:51:25