CF1846E2 Rudolf and Snowflakes (hard version)

This is the hard version of the problem. The only difference is that in this version $ n \le 10^{18} $ . One winter morning, Rudolf was looking thoughtfully out the window, watching the falling snowflakes. He quickly noticed a certain symmetry in the configuration of the snowflakes. And like a true mathematician, Rudolf came up with a mathematical model of a snowflake. He defined a snowflake as an undirected graph constructed according to the following rules: - Initially, the graph has only one vertex. - Then, more vertices are added to the graph. The initial vertex is connected by edges to $ k $ new vertices ( $ k > 1 $ ). - Each vertex that is connected to only one other vertex is connected by edges to $ k $ more new vertices. This step should be done at least once. The smallest possible snowflake for $ k = 4 $ is shown in the figure. After some mathematical research, Rudolf realized that such snowflakes may not have any number of vertices. Help Rudolf check whether a snowflake with $ n $ vertices can exist.

The first line of the input contains an integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Then follow the descriptions of the test cases. The first line of each test case contains an integer $ n $ ( $ 1 \le n \le 10^{18} $ ) — the number of vertices for which it is necessary to check the existence of a snowflake.

Output $ t $ lines, each of which is the answer to the corresponding test case — "YES" if there exists such $ k > 1 $ that a snowflake with the given number of vertices can be constructed; "NO" otherwise.