CF1202F You Are Given Some Letters...

You are given $ a $ uppercase Latin letters 'A' and $ b $ letters 'B'. The period of the string is the smallest such positive integer $ k $ that $ s_i = s_{i~mod~k} $ ( $ 0 $ -indexed) for each $ i $ . Note that this implies that $ k $ won't always divide $ a+b = |s| $ . For example, the period of string "ABAABAA" is $ 3 $ , the period of "AAAA" is $ 1 $ , and the period of "AABBB" is $ 5 $ . Find the number of different periods over all possible strings with $ a $ letters 'A' and $ b $ letters 'B'.

The first line contains two integers $ a $ and $ b $ ( $ 1 \le a, b \le 10^9 $ ) — the number of letters 'A' and 'B', respectively.

Print the number of different periods over all possible strings with $ a $ letters 'A' and $ b $ letters 'B'.

All the possible periods for the first example: - $ 3 $ "BBABBA" - $ 4 $ "BBAABB" - $ 5 $ "BBBAAB" - $ 6 $ "AABBBB" All the possible periods for the second example: - $ 3 $ "BAABAABA" - $ 5 $ "BAABABAA" - $ 6 $ "BABAAABA" - $ 7 $ "BAABAAAB" - $ 8 $ "AAAAABBB" Note that these are not the only possible strings for the given periods.