P5088 Rectangle

Xiao Ben did very well on the monthly exam. As a reward, the teacher gave him a laser pointer.

However, the teacher never gives Xiao Ben a prize for free. He told Xiao Ben that the angle of reflection equals the angle of incidence, and asked him to solve the following problem. Given a rectangle whose length-to-width ratio is $N:M$. A laser beam is emitted from the top-left corner, and the angle between the beam and the side of length $N$ is $\zeta°$ ($0\le \zeta° \le 90$). It also satisfies $\cot \zeta° = A:B$. Find the minimum number of reflections needed for the beam to enter (after reflections) any one of the four corners again. 

Two lines. The first line contains two numbers $N$ and $M$, representing the ratio of the length to the width. The second line contains two numbers $A$ and $B$, representing $\cot\zeta°$.

One positive integer, representing the minimum number of reflections needed.

For $10\%$ of the testdata, $A=B=1$. For another $10\%$ of the testdata, $N=M$. For $50\%$ of the testdata, $0\le A,B,M,N\le10^5$. For $100\%$ of the testdata, $0\le A,B,M,N\le10^{10}$. Translated by ChatGPT 5