Problem Statement

Iwai Seijin plans to work part-time at an okonomiyaki restaurant for at most $N$ days starting now. Initially, his skill at cooking okonomiyaki is $X$, and he has $0$ yen.
Each day, he chooses one of the following two actions.

• Attend training: His skill increases by $Y$, and he earns $P$ yen as the daily wage for the training period.
• Perform regular duties: He earns $Q$ yen as the daily wage. However, with probability $ \frac{1}{\text{skill}} $, he pours egg on a customer. If he pours egg on a customer, he chooses one of the following.
  • Pay $R$ yen to serve the customer a complimentary lemon sour and cover up the incident (his money may become negative in this case).
  • Do not cover it up; the manager finds out, and he is fired that same day.
  Note that even if he is fired, he still receives that day's wage of $Q$ yen.

The job ends when $N$ days have passed or when he is fired.
Iwai Seijin chooses his actions so as to maximize the expected value of his money at the time the job ends. Find the expected value of his money when the job ends.

You are given $T$ test cases. Find the answer for each of them.

Constraints

All input values are integers
$1 \leq T \leq 300$
$1 \leq N \leq 10^{12}$
$1 \leq X, Y \leq 100$
$1 \leq P \leq Q \leq 10^5$
$1 \leq R \leq 10^5$

Input

The input is given from standard input in the following format, where $\mathrm{case}_i$ denotes the $i$-th test case.

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Each test case is given in the following format.

$N$
$X\ Y$
$P\ Q\ R$

Output

Output $T$ lines.
On the $i$-th line, output the expected value of his money at the end of the job for the $i$-th test case.
Your answer is judged correct if the relative error is at most $10^{-8}$.

Sample

5
1
1 1
1 2 10000
2
3 1
1 2 10000
2
3 1
1 2 1
3000
1 1
800 1000 200
1000000000000
100 100
100000 100000 100000

2.0000000000
3.3333333333
3.6666666667
2978490.9090909091
100000000000000000.0000000000