There is a special square room with mirrors on each of the four walls. Except for the southwest corner, there are receptors on each of the remaining corners, numbered 0
, 1
, and 2
.
The square room has walls of length p
and a laser ray from the southwest corner first meets the east wall at a distance q
from the 0^{th}
receptor.
Given the two integers p
and q
, return the number of the receptor that the ray meets first.
The test cases are guaranteed so that the ray will meet a receptor eventually.
Example 1:
Input: p = 2, q = 1
Output: 2
Explanation: The ray meets receptor 2 the first time it gets reflected back
to the left wall.
Example 2:
Input: p = 3, q = 1
Output: 1
Constraints:
1 <= q <= p <= 1000


class Solution:
def mirrorReflection(self, p, q):
k = 1
while k*q%p:
k += 1
if k%2 == 1 and (k*q//p)%2 == 0:
return 0
if k%2 == 1 and (k*q//p)%2 == 1:
return 1
if k%2 == 0 and (k*q//p)%2 == 1:
return 2