Acceleration
Imagine a 1-D coordinate system. Bob is at the origin at time t = 0. Bob wants to go to point X (X > 0) in his car. At each point with coordinate x (except the origin) there is a force equal to a given function F(x) which pushes him towards origin. Assuming his car have unit mass, what is the minimum value of acceleration his car needs to be able to travel to point X.
Please output the infimum of set of acceleration values, which will enable Bob to travel to point X. The infimum of a set A of numbers is the upper bound on values of all real numbers y such that:
y < x ∀ x ∈ A
Also note that, Bob always tries to go towards point X from the origin. He never tries to go towards negative side of the coordinate axis and come back.
For the purpose, the function F(x) is a polynomial in x.
Input
First line contains T, the number of test cases. For each test case, the first line contains N; the degree of polynomial F(x) and X the target coordinate where Bob wants to go. Next line contains N + 1 space separated real numbers, i-th number referring to the coefficient of x^i in F(x) for 0 ≤ i ≤ N. It is known that 1 ≤ T ≤ 10000, 0 ≤ N ≤ 5, 0 < X ≤ 10, 0 ≤ coefficients ≤ 1.
Output
Output contains T lines, each containing the infimum of set of acceleration values for the corresponding test case. Please output the value, rounded to 3 decimal places.