Six Equations

Six simple equations are given. The unknowns $x_1$, $x_2$, $x_3$, $x_5$, $x_6$, $x_7$ are all primes that are at least 2 and at most 20,000,000.

• $c_1 = x_1 x_2$
• $x_4 = \dfrac{c_4}{x_1}$
• $c_3 = x_6 x_7$
• $x_8 = \dfrac{c_2}{x_7}$
• $c_5 = x_2 x_3$
• $c_6 = x_6 x_5$

Every $c_1$ through $c_6$ is a positive integer that does not exceed 20,000,000 squared. The values $x_4$ and $x_8$ are fixed by the two equations above. Nothing requires them to be prime, and they are not printed.

Given $c_1$, $c_2$, $c_3$, $c_4$, $c_5$, $c_6$, write a program that finds $x_1$, $x_2$, $x_3$, $x_5$, $x_6$, $x_7$. Only inputs that have a solution are given.

The first line contains $c_1$, $c_2$, $c_3$, $c_4$, $c_5$, $c_6$ separated by spaces. Here $c_1 \neq c_5$ and $c_3 \neq c_6$.

Print $x_1$, $x_2$, $x_3$, $x_5$, $x_6$, $x_7$ in this order on one line, separated by single spaces. Because $c_1 \neq c_5$ and $c_3 \neq c_6$, the six values are determined uniquely.