SP2002 RNG - Random Number Generator

LoadingTime got a RNG (_Random Number Generator_) from his classmate several weeks ago. And he spent a lot of time study it. He found that RNG can generate a real number in range \[-**S**,**S**\] by executing following steps. First RNG generates n integer **X** $ _{1} $ ..**X** $ _{n} $ , the sum of which is equal to **S**. Then for each **X** $ _{i} $ , it generates a real number in range \[-**X** $ _{i} $ ,**X** $ _{i} $ \] randomly. The output (a real number) of RNG will be the sum of the **N** generated real numbers. LoadingTime noticed that the distribution of the output was very interesting, and he wanted to know: for given **N** and **X**, what's the probability that the generated number is in range \[**A**,**B**\]. Could you help him?

The first line contains an integer T representing the number of test cases. For each test case, the first line contains three integers **N**, **A**, **B**(1 ≤ **N** ≤ 10, -100 ≤ **A** ≤ **B** ≤ 100) In the second line of the test case, you are given **X** $ _{1} $ ...**X** $ _{n} $ (1 ≤ **X** $ _{i} $ ≤ 10).

For each test case, print a line contains a real number representing the probablity as the problem required. It must be printed with exactly nine decimal places.