A12833. 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.