You Are Given Some Letters...

1000ms

262144K

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'.

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'.

Sample Input:

2 4

Sample Output:

Sample Input:

5 3

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1202F