#P1202F. You Are Given Some Letters...
You Are Given Some Letters...
Description
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'.
Input
The first line contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$) — the number of letters 'A' and 'B', respectively.
Output
Print the number of different periods over all possible strings with $a$ letters 'A' and $b$ letters 'B'.
Samples
2 4
4
5 3
5
Note
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.