F. You Are Given Some Letters...
binary search; implementation; math
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.