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'.

-----Examples-----

Input 2 4

Output 4

Input 5 3

Output 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.