Zeroes#10658
Santa Claus is preparing for the New Year. He wants to buy some positive number of gifts so that he can distribute them evenly (without remainder) among all obedient children. However, he does not yet know how many obedient children there will be — he only knows that this number lies between and inclusive. Therefore, he wants to buy the minimal positive number of gifts that can be divided evenly among any number of children , where x \in \{a, a+1, \ldots, b\}.
He has found this (possibly enormous) number of gifts but is unsure whether he is correct, so he asks you to check it. Can you tell him how many zeros should be at the end of this number?
The input contains one line with two integers and (1 \leq a \leq b \leq 10^{18}).
Print one integer: the number of zeros at the end of the number of gifts Santa Claus should buy.
Example 1
Example 2
First example: If there could be any number of children from to , then Santa Claus needs to buy at least gifts (since this is the smallest number divisible by all of 1, 2, 3, 4, 5, and ), and the number ends with one zero.
Second example: If there can be or children, Santa Claus needs to buy gifts.
Block 1 (6 points): b \leq 16. Block 2 (7 points): b \leq 40. Block 3 (9 points): a = 1 and b \leq 200. Block 4 (12 points): b-a \leq 10^6. Block 5 (17 points): a = 1. Block 6 (49 points): without additional constraints.