Laser Beam

Time limit1sMemory limit1024 MB

Summary

Given mirror angle alpha and beam angle beta, count how many times a laser beam reflects off the two mirrors before it travels off to infinity.

Level: Medium5 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

Two infinite flat mirrors are placed at an angle $\alpha$ to each other. Viewed from the side, they appear as two lines on a plane. A laser beam is fired through a tiny hole in one of the mirrors at an angle $\beta$ , as shown in the figure below.

Count the number of times the beam reflects off the mirrors before it travels off to infinity. The angle of incidence always equals the angle of reflection. The hole is extremely small, so if the beam happens to hit the hole, it still reflects according to the usual rules.

Input

Two integers $\alpha$ and $\beta$ are given. Both are angles in degrees, with $1 \le \alpha \le 179$ and $1 \le \beta \le 179$ .

Output

Print one integer, the number of reflections.

Hint

In the first example, the beam reflects as shown below.

Examples3

Example 1
Input
```
30 35
```
Expected output
```
4
```
Example 2
Input
```
90 90
```
Expected output
```
0
```
Example 3
Input
```
30 60
```
Expected output
```
3
```