AT_past18_c 信号

There are two traffic lights, light $ 1 $ and light $ 2 $ . Light $ i $ $ (i=1,2) $ repeatedly shows green light for $ B_i $ seconds and red light for $ R_i $ seconds. In other words, if light $ i $ turns from red to green at some point, it remains green for the next $ B_i $ seconds, and then remains red for the succeeding $ R_i $ seconds; this way, it alternates between green and red light indefinitely. Now, the two lights have simultaneously turned from red to green. Within the next $ T $ seconds, how many seconds do both light $ 1 $ and light $ 2 $ show green?

The input is given from Standard Input in the following format: > $ B_1 $ $ R_1 $ $ B_2 $ $ R_2 $ $ T $

Print the duration, in seconds as an integer, for which both light $ 1 $ and light $ 2 $ show green within the $ T $ seconds right after the two lights simultaneously turn from red to green.

### Sample Explanation 1 Within the $ 10 $ seconds right after the two traffic lights simultaneously turn from red to green, the lights transition as follows: - From $ 0 $ to $ 2 $ seconds after the switch, both light $ 1 $ and light $ 2 $ are green. - From $ 2 $ to $ 5 $ seconds after the switch, light $ 1 $ is red and light $ 2 $ is green. - From $ 5 $ to $ 6 $ seconds after the switch, light $ 1 $ is green and light $ 2 $ is red. - From $ 6 $ to $ 7 $ seconds after the switch, both light $ 1 $ and light $ 2 $ are green. - From $ 7 $ to $ 10 $ seconds after the switch, light $ 1 $ is red and light $ 2 $ is green. Therefore, both lights show green from $ 0 $ to $ 2 $ and from $ 6 $ to $ 7 $ seconds after the switch, for a total of $ 3 $ seconds. ### Sample Explanation 2 Both lights show green for $ 100 $ seconds, followed by red for $ 100 $ seconds; this sequence repeats indefinitely. ### Constraints - $ 1\leq B_i,R_i\leq 100 $ - $ 1\leq T\leq 10^4 $ - All input values are integers.