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Once again the time dawns to demonstrate the sheer power of the Illuminati. To do so, it was decided to build an n-dimensional hyper-step pyramid using n-dimensional blocks:
To prove their might even further the Illuminati leaders have decided to add two more requirements:
Figure H.1: A 3-dimensional hyper pyramid with 3 steps consisting of 14 blocks in total.
The input consists of:
If a hyper-step pyramid matching all the requirements exists, output a single line with two integers n and s, the dimension of the pyramid and its number of steps. If none exists, output impossible. If multiple solutions exist, any will be accepted.