Score : $200$ points

问题描述

有一个容器，其中装有 $A$ 个青色球。Takahashi 将根据需要重复执行以下操作任意次数（可能为零次）：

• 向容器中添加 $B$ 个青色球和 $C$ 个红色球。

Takahashi 的目标是达到一种状态，使得容器中青色球的数量最多是红色球数量的 $D$ 倍。

确定该目标是否可以实现。如果目标可以实现，则找出实现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

There is a container with $A$ cyan balls. Takahashi will do the following operation as many times as he likes (possibly zero times):

• add $B$ cyan balls and $C$ red balls into the container.

Takahashi's objective is to reach a situation where the number of cyan balls in the container is at most $D$ times the number of red balls in it.

Determine whether the objective is achievable. If it is achievable, find the minimum number of operations needed to achieve it.

Constraints

• $1 \leq A,B,C,D \leq 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $C$ $D$

Output

If Takahashi's objective is achievable, print the minimum number of operations needed to achieve it. Otherwise, print -1.

Sample Input 1

5 2 3 2

Sample Output 1

2

Before the first operation, the container has $5$ cyan balls and $0$ red balls. Since $5$ is greater than $0$ multiplied by $D=2$, Takahashi's objective is not yet achieved.

Just after the first operation, the container has $7$ cyan balls and $3$ red balls. Since $7$ is greater than $3$ multiplied by $2$, the objective is still not achieved.

Just after the second operation, the container has $9$ cyan balls and $6$ red balls. Since $9$ is not greater than $6$ multiplied by $2$, the objective is achieved.

Thus, the answer is $2$.

Sample Input 2

6 9 2 3

Sample Output 2

-1

No matter how many times Takahashi repeats the operation, his objective will never be achieved.

update @ 2024/3/10 09:20:09