C2. Good Numbers (hard version)
binary search; greedy; math; meet-in-the-middle
The only difference between easy and hard versions is the maximum value of \(n\).You are given a positive integer number \(n\). You really love good numbers so you want to find the smallest good number greater than or equal to \(n\).The positive integer is called good if it can be represented as a sum of distinct powers of \(3\) (i.e. no duplicates of powers of \(3\) are allowed).For example: \(30\) is a good number: \(30 = 3^3 + 3^1\), \(1\) is a good number: \(1 = 3^0\), \(12\) is a good number: \(12 = 3^2 + 3^1\), but \(2\) is not a good number: you can't represent it as a sum of distinct powers of \(3\) (\(2 = 3^0 + 3^0\)), \(19\) is not a good number: you can't represent it as a sum of distinct powers of \(3\) (for example, the representations \(19 = 3^2 + 3^2 + 3^0 = 3^2 + 3^1 + 3^1 + 3^1 + 3^0\) are invalid), \(20\) is also not a good number: you can't represent it as a sum of distinct powers of \(3\) (for example, the representation \(20 = 3^2 + 3^2 + 3^0 + 3^0\) is invalid). Note, that there exist other representations of \(19\) and \(20\) as sums of powers of \(3\) but none of them consists of distinct powers of \(3\).For the given positive integer \(n\) find such smallest \(m\) (\(n \le m\)) that \(m\) is a good number.You have to answer \(q\) independent queries.
The first line of the input contains one integer \(q\) (\(1 \le q \le 500\)) — the number of queries. Then \(q\) queries follow.The only line of the query contains one integer \(n\) (\(1 \le n \le 10^{18}\)).
For each query, print such smallest integer \(m\) (where \(n \le m\)) that \(m\) is a good number.