Competitions

# Zeroes

Santa Claus is already preparing for the New Year 2022. He wants to buy a certain positive amount of gifts so that he can distribute them evenly (without a remainder) among all obedient children. However, he does not know now how many obedient children will be - he only knows that this number ranges from $a$ to $b$. Therefore, he wants to buy a \emph{minimal} positive number of gifts that can be divided between any number of children $x$, where $x \in \{a,a+1,...,b\}$. He found this (possibly huge) number of gifts, but he is not sure of the correctness, so he asks you to check it. Are you able to tell him how many zeros there should be at the end of this number? \InputFile One line contains two integers $a$ and $b$ ($1 \le a \le b \le 10^{18}$). \OutputFile Print one integer - the number of zeros at the end of the number of gifts that Santa Claus should buy. \Note First example: If there can be from 1 to 6 children, then Santa Claus will buy at least 60 gifts (since this is the smallest number that is divisible by 1, 2, 3, 4, 5 and 6 at the same time), and the number 60 has one zero at the end. Second example: there may be 10 or 11 children, Santa Claus has to buy 110 gifts. \Scoring Block 1 (6 points): $b \le 16$. Block 2 (7 points): $b \le 40$. Block 3 (9 points): $a = 1$ and $b \le 200$. Block 4 (12 points): $b-a \le 10^6$. Block 5 (17 points): $a = 1$. Block 6 (49 points): without additional restrictions.
Time limit 1 second
Memory limit 256 MiB
Input example #1
1 6
Output example #1
1
Input example #2
10 11
Output example #2
1
Author Anton Tsypko