Breaking the Equations

You are given a set $A = \{a_1, a_2, a_3, \dots, a_n\}$. Every element of $A$ is an integer that is at least 0.

Consider these six equations.

• $c_1 = x_1 + x_2$
• $x_4 = x_3 + x_1$
• $x_5 = x_6 + x_7$
• $x_{11} = x_8 + x_9$
• $x_6 = x_2 + x_{10}$
• $x_{12} = x_9 + c_2$

$c_1$ and $c_2$ are integer constants. Given $c_1$ and $c_2$, write a program that solves the equations, that is, find all twelve values $x_1$ through $x_{12}$. Every $x_i$ must be an element of $A$. Two different $x_i$ may take the same value. Only inputs whose equations can be solved are given.

The first line contains $n$, $c_1$, and $c_2$. Each of the next $n$ lines contains one $a_i$. $12 \le n \le 7{,}000$, and each $a_i$ is a 32-bit integer.

Print 12 lines in total: $x_1$ on the first line, $x_2$ on the second, and so on down to $x_{12}$ on the twelfth.

If more than one solution exists, compare the tuples $(x_1, x_2, \dots, x_{12})$ position by position from the front and print only the lexicographically smallest one.