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Non-divisible 2-3 Power Sums
Every positive integer N can be written in at least one way as a sum of terms of the form (2a)(3b) where no term in the sum exactly divides any other term in the sum. For example:
Note from the example of 31 that the representation is not unique.
Write a program which takes as input a positive integer N and outputs a representation of N as a sum of terms of the form (2a)(3b).
The first line of input contains a single integer C (1 ≤ C ≤ 1000) which is the number of datasets that follow.
Each dataset consists of a single line of input containing a single integer N (1 ≤ N < 231), which is the number to be represented as a sum of terms of the form (2a)(3b).
For each dataset, the output will be a single line consisting of: The dataset number, a single space, the number of terms in your sum as a decimal integer followed by a single space followed by representations of the terms in the form
6 1 7 31 7776 531441 123456789
1 1 [0,0] 2 2 [2,0] [0,1] 3 3 [4,0] [0,2] [1,1] 4 1 [5,5] 5 1 [0,12] 6 8 [3,13] [4,12] [2,15] [7,8] [9,6] [0,16] [10,5] [15,2]
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