Math teacher Mr. Matsudaira is teaching expansion and factoring of polynomials to his students. Last week he instructed the students to write two polynomials (with a single variable \textbf{x}), and to report \textbf{GCM} (greatest common measure) of them as a homework, but he found it boring to check their answers manually. So you are asked to write a program to check the answers. Hereinafter, only those polynomials with integral coefficients, called integral polynomials, are considered. When two integral polynomials \textbf{A} and \textbf{B} are given, an integral polynomial \textbf{C} is a common factor of \textbf{A} and \textbf{B} if there are some integral polynomials \textbf{X} and \textbf{Y} such that \textbf{A = CX} and \textbf{B = CY}. \textbf{GCM} of two integral polynomials is a common factor which has the highest degree (for \textbf{x}, here); you have to write a program which calculates the \textbf{GCM} of two polynomials. It is known that \textbf{GCM} of given two polynomials is unique when constant multiplication factor is ignored. That is, when \textbf{C }and \textbf{D} are both \textbf{GCM} of some two polynomials \textbf{A} and \textbf{B}, \textbf{p}×\textbf{C} = \textbf{q}×\textbf{D} for some nonzero integers \textbf{p} and \textbf{q}. \InputFile The input consists of multiple datasets. Each dataset constitutes a pair of input lines, each representing a polynomial as an expression defined below. \begin{enumerate} \item A \textit{primary} is a variable \textbf{x}, a sequence of digits \textbf{0}--\textbf{9}, or an expression enclosed within (...). Examples: \textbf{x}, \textbf{99},\textbf{(x+1)}. \item A \textit{factor} is a primary by itself or a primary followed by an exponent. An exponent consists of a symbol \textbf{^}followed by a sequence of digits \textbf{0}--\textbf{9}. Examples: \textbf{x^05}, \textbf{1^15}, \textbf{(x+1)^3}. \item A \textit{term} consists of one or more adjoining factors. Examples: \textbf{4x}, \textbf{(x+1)(x-2)}, \textbf{3(x+1)^2}. \item An \textit{expression} is one or more terms connected by either \textbf{+} or \textbf{-}. Additionally, the first term of an expression may optionally be preceded with a minus sign \textbf{-}. Examples: \textbf{-x+1}, \textbf{3(x+1)^2-x(x-1)^2}. \end{enumerate} Integer constants, exponents, multiplications (adjoining), additions (\textbf{+}) and subtractions/negations (\textbf{-}) have their ordinary meanings. A sequence of digits is always interpreted as an integer constant. For example, \textbf{99} means \textbf{99}, not \textbf{9}×\textbf{9}. Any subexpressions of the input, when fully expanded normalized, have coefficients less than \textbf{100} and degrees of\textbf{x} less than \textbf{10}. Digit sequences in exponents represent non-zero values. All the datasets are designed so that a standard algorithm with \textbf{32}-bit two’s complement integers can solve the problem without overflows. The end of the input is indicated by a line containing a period. \OutputFile For each of the dataset, output \textbf{GCM} polynomial expression in a line, in the format below. \textbf{c_0x^p_0 ± c_1x^p_1...± c_nx^p_n} Where \textbf{c_i} and \textbf{p_i} (\textbf{i = 0}, ..., \textbf{n}) are positive integers with \textbf{p_0} > \textbf{p_1} > ... > \textbf{p_n}, and the greatest common divisor of \textbf{\{c_i | i = 0, ..., n\}} is \textbf{1}. Additionally: \begin{enumerate} \item When \textbf{c_i} is equal to \textbf{1}, it should be omitted unless corresponding \textbf{p_i} is \textbf{0}, \item \textbf{x^0} should be omitted as a whole, and \item \textbf{x^1} should be written as \textbf{x}. \end{enumerate}