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In the present problem, we always assume that all the polynomials mentioned have the following properties (take f(x) for example ):
(1) 0 < deg(f) <= 20, so we can assume that f(x) has the following form:
(2) ai ( i=0,1,...,n ) is integer, and ?2^31<=ai<=2^31-1;
(3) an = 1.
We call a polynomial G(x) "good" polynomial, when there is no polynomial F(x) such that
Given a polynomial f(x), it is known that f(x) can be factorized as follow:
f(x)=GtmtGt-1mt-1...G1m1 (Gi is good and mt>mt-1>...>m1>=1)
It抯 easy to prove that this way of factorizing is unique. You job is to factorize the given polynomials in this way.
To make input and output easy, a polynomial f(x)
is represented as
In this representation, we use (n+2) integers, which are separated by single blanks.
The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Every case gives a polynomial in a single line.
For each test case, output the corresponding result in the following form (where the meaning of those characters is taken as just mentioned):
2 5 1 -3 4 -4 3 -1 2 1 -1 -2
2 3 1 1 -1 1 2 1 0 1 1 1 2 1 -1 -2
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