F. You Are Given Some Letters...time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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'.InputThe first line contains two integers a and b (1 \le a, b \le 10^9) — the number of letters 'A' and 'B', respectively.OutputPrint the number of different periods over all possible strings with a letters 'A' and b letters 'B'.ExamplesInput
2 4
Output
4
Input
5 3
Output
5
NoteAll 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.
2 4

4 
['binary search', 'implementation', 'math', '*2700']