$$$Da7doo7$$$ believed he had mastered competitive programming contests, so he decided to turn his attention to playing basketball.
$$$Da7doo7$$$ intends to shoot $$$n$$$ balls into the basket. The probability of him scoring the first shot is $$$\frac{p_0}{q_0}$$$.
For subsequent shots, his probability of scoring depends on whether he made the previous shot or not:
If he scored shot $$$i-1$$$, the probability of scoring shot $$$i$$$ is $$$\frac{p_1}{q_1}$$$.
If he missed shot $$$i-1$$$, the probability of scoring shot $$$i$$$ is $$$\frac{p_2}{q_2}$$$.
$$$Da7doo7$$$ is asking for your help to find the expected value of the number of balls that will score.
We can show that the answer can be written in the form $$$\frac{P}{Q}$$$ where $$$P, Q$$$ are coprime integers and $$$Q \neq 0 \bmod 998244353$$$. Output the value of $$$(P \cdot Q^{-1})$$$ modulo $$$998244353$$$.
The first line contains a single integer $$$T$$$ ($$$1 \le T \le 5 \times 10^4$$$) — the number of testcases.
The first line of each testcase contains an integer $$$n$$$ ($$$1 \le n \le 10^{12}$$$) — the number of balls he will shoot.
The second line of each testcase contains six integers $$$p_0,q_0,p_1,q_1,p_2,q_2$$$ ($$$0 \le p_0,p_1,p_2 \le 10^{3}$$$ , $$$1 \le q_0,q_1,q_2 \le 10^{3}$$$).
An integer representing the expected value of the number of balls that will score, modulo $$$998244353$$$.
525 10 2 10 3 10107 10 5 10 2 1051 5 7 10 9 101001 1 1 10 1 110000000075 100 55 100 23 100
249561089 965715715 403450441 210477862 330198862
