1711 - Random at Random
Time Limit : 1 Second
Memory Limit : 128 MB
Xiao Hua is a student who loves running. However, he is too fat to run fast.
As a straight A student of science and engineering, Xiao Hua developed a running-helper one day to accelerate himself while running. He called it the HKJA(Hong Kong Journalist Accelerator).
The HKJA’s operating mechanism is as follows: each acceleration contains n independent sections (where n is a non-negative random variable). Its expectation is μn and the variance is σn2 . During the ith independent acceleration-section, the HKJA gives the user a velocity increment values ai(where ai~N(μa.σa2) ). All the ai is in i.i.d.(independent identical distribution). The result of the final acceleration is the sum of all ai , denoted as S.
It is not difficult to find that the total speed increment S is also a random variable.
In order to test whether the acceleration effect is "steady", Xiao Hua would like to know, given the features of distribution which n and ai obey (given the expectations and variance), how much is the variance of random variable S ?
The first line of the input file is a positive integer T（1<=T<=20），indicating that there are T test cases.
As for each test case：there is only one line contains four integers representing μn，σn2，μa，σa2.
For each set of samples, output the variance of the random variable S.
- sample input
4 2 0 10 4 2 3 6 4 5 2 -5 3 3 4 3 0
- sample output
8 116 65 36
Standard input and output.
n~N(μ,σ2)means random variable nobeys normal distribution. The expectation is μ, the variance is σ2，it is obvious that the variance isnon-negative.