Picture by Nevit via Wikimedia Commons
Your hometown has hired some contractors – including you!
– to manage its municipal pipe network. They built the network,
at great expense, to supply Flubber to every home in town.
Unfortunately, nobody has found a use for Flubber yet, but
never mind. It was a Flubber network or a fire department, and
honestly, houses burn down so rarely, a fire department hardly
seems necessary.
In the possible event that somebody somewhere decides they
want some Flubber, they would like to know how quickly it will
flow through the pipes. Measuring its rate of flow is your
job.
You have access to one of the pipes connected to the
network. The pipe is $l$
meters long, and you can start the flow of Flubber through this
pipe at a time of your choosing. You know that it flows with a
constant realvalued speed, which is at least $v_1$ meters/second and at most
$v_2$ meters/second. You
want to estimate this speed with an absolute error of at most
$\frac{t}{2}$
meters/second.
Unfortunately, the pipe is opaque, so the only thing you can
do is to knock on the pipe at any point along its length, that
is, in the closed realvalued range $[0,l]$. Listening to the sound of the
knock will tell you whether or not the Flubber has reached that
point. You are not infinitely fast. Your first knock must be at
least $s$ seconds after
starting the flow, and there must be at least $s$ seconds between knocks.
Determine a strategy that will require the fewest knocks, in
the worst case, to estimate how fast the Flubber is flowing.
Note that in some cases the desired estimation might be
impossible (for example, if the Flubber reaches the end of the
pipe too quickly).
Input
The input consists of multiple test cases. The first line of
input contains an integer $c$ ($1
\leq c \leq 100$), the number of test cases. Each of the
next $c$ lines describes
one test case. Each test case contains the five integers
$l$, $v_1$, $v_2$, $t$ and $s$ ($1
\leq l, v_1, v_2, t, s \leq 10^9$ and $v_1 < v_2$), which are described
above.
Output
For each test case, display the minimal number of knocks
required to estimate the flow speed in the worst case. If it
might be impossible to measure the flow speed accurately
enough, display impossible
instead.
Sample Input 1 
Sample Output 1 
3
1000 1 30 1 1
60 2 10 2 5
59 2 10 2 5

5
3
impossible
