Factorization of Quadratic Formula

As the first step in algebra, students learn quadratic formulas and their factorization. Factorization is often a heavy burden for them. A large number of students never master it, so they cannot appreciate the elegance of advanced algebra. Factorization may even increase the number of people who hate mathematics.

This problem asks you to write a program that helps students in an algebra course. Given a quadratic formula, the program reports whether it can be factorized into two linear formulas, and if so, gives the factorization. All coefficients in this problem are integers.

The coefficients $a$, $b$, and $c$ of the quadratic formula $ax^2 + bx + c$ are given. They are integers with absolute values at most 10000. The program must find integers $p$, $q$, $r$, and $s$ such that $ax^2 + bx + c = (px + q)(rx + s)$. Since only integer coefficients are allowed, some formulas cannot be factorized this way. In that case, the program reports that the factorization is impossible.

The input is a sequence of lines, each describing one quadratic formula. Each line has the format

$a$ $b$ $c$

where $a$, $b$, and $c$ are integers separated by spaces. They satisfy the following inequalities.

$0 \lt a \le 10000$

$-10000 \le b \le 10000$

$-10000 \le c \le 10000$

The greatest common divisor of $a$, $b$, and $c$ is 1. No integer $k$ greater than 1 divides all three.

The end of input is a line containing three 0's.

For each input line, print the four integers $p$, $q$, $r$, and $s$ on one line, in this order, if a factorization exists. Separate the integers with one or more spaces. If the factorization is impossible, print only the word "Impossible".

The four coefficients must satisfy the following conditions.

$p > 0$

$r > 0$

$p > r$, or $p = r$ and $q \ge s$

These conditions, together with the fact that the greatest common divisor of $a$, $b$, and $c$ is 1, make the answer unique. Once you find a factorization, you do not need to look for another one.