Hyper Illuminati#11632
Once again, the time has come to demonstrate the overwhelming power of the Illuminati. To do so, it was decided to build an -dimensional hyper-step pyramid using -dimensional blocks:
All the steps of the pyramid are -dimensional hypercuboids.
Every step has a height of exactly block in the -th dimension.
The pyramid has steps, and the base step is blocks long in each of the other n - 1 dimensions.
Every subsequent higher step is block shorter in each of the n - 1 dimensions than the step below it.
The top step is exactly block.
To further demonstrate their might, the Illuminati leaders have decided to add two more requirements:
must be at least .
The number of blocks used to build the pyramid must be a meaningful number.
A -dimensional hyper pyramid with steps consisting of blocks in total.
One integer (1 \le m \le 10^{16}). This integer is the meaningful number chosen by the leaders.
If a hyper-step pyramid matching all the requirements exists, output a single line with two integers and : the dimension of the pyramid and its number of steps. If none exists, output impossible. If multiple solutions exist, any one will be accepted.
Example 2
Example 1
Example 3
Example 4