P17736 [ICPC 2019 Xuzhou R] The Answer to the Ultimate Question of Life, The Universe, and Everything.

For decades, scientists have wondered whether each of the numbers from 0 to 100 could be represented as the sum of three cubes, where a cube is the same number multiplied together three times. 42 was the last number without a proven solution — until now. The solution is $(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42$ Now, Yen-Jen is suspicious of the existence of other solutions. But, the solutions are not so trivial to find out. Yen-Jen wants to find out easysolutions first. That is, for the equation $a^3 + b^3 + c^3 = x$,Yen-Jen wants to find out at least one solution for each integer $x$ in $[0, 200]$,where $|a|, |b|, |c| \le 5000$. Since Yen-Jen is still busy preparing the test data of some(this?) problem, pleasehelp him find out at least one solution for each $x$ or tell him that thesolution doesn't exist when $|a|, |b|, |c| \le 5000$.

The first line contains an integer $T$ indicating the number of $x$ to bechecked.Following $T$ lines each contains one integer $x$. - $1 \le T \le 10$ - $0 \le x \le 200$

For each test case, output one line containing three space-separated integers $a, b, c$ such that $a^3 + b^3 + c^3 = x$ and $|a|, |b|, |c| \le 5000$. If thesolution doesn't exist, output `impossible`.