RNG

Hyunsu is making a new adventure game featuring pirates and monkeys. To drive its many random elements, the game uses a random number generator, RNG for short.

Given the previous random number $x$, the RNG produces the next number $y$ by

$y = ax^2 + bx + c \pmod{2^n}$

where $a$, $b$, $c$, and $n$ are integers.

While debugging, Hyunsu sees the current random number $y$ in the debug console and wants to recover the number $x$ that was generated immediately before it.

Given the current number $y$ and the constants $a$, $b$, $c$, $n$, find the previous number $x$ ($0 \le x < 2^n$) satisfying the equation above. If exactly one such $x$ exists, print it; if none exists or two or more exist, print No unique solution.

The first line contains the number of test cases $T$.

Each test case is given on one line as five space-separated integers $y$, $a$, $b$, $c$, $n$. ($0 \le y, a, b, c < 2^n$, $1 \le n \le 31$)

For each test case, print the previous number $x$ satisfying the equation, one per line.

If such an $x$ is not unique (there is none, or there are two or more), print No unique solution instead.