B. Fair Numbers
brute force; number theory
We call a positive integer number fair if it is divisible by each of its nonzero digits. For example, \(102\) is fair (because it is divisible by \(1\) and \(2\)), but \(282\) is not, because it isn't divisible by \(8\). Given a positive integer \(n\). Find the minimum integer \(x\), such that \(n \leq x\) and \(x\) is fair.
The first line contains number of test cases \(t\) (\(1 \leq t \leq 10^3\)). Each of the next \(t\) lines contains an integer \(n\) (\(1 \leq n \leq 10^{18}\)).
For each of \(t\) test cases print a single integer — the least fair number, which is not less than \(n\).
Explanations for some test cases: In the first test case number \(1\) is fair itself. In the second test case number \(288\) is fair (it's divisible by both \(2\) and \(8\)). None of the numbers from \([282, 287]\) is fair, because, for example, none of them is divisible by \(8\).