There are n balls in the urn, each of them has one of k colors, and the number of balls of each color, like the color itself, is known and written on a separate plate. Dima, who started to study the theory of probability, decided to play a trick on his comrades and took advantage of the opportunity, unnoticed from the rest, replaced all the balls of some color that he did not like with balls of absolutely different colors, each of which is missing in the inscriptions on the plates, and hid the tablet itself.

Now to everyone who comes into the audience, he asks the same question:

• Tell me please, with what probability will you get from the urn a ball with a color not indicated on the plates?

Your task is to write a program that quickly answers Dima's questions.

Input

The first line contains the number of friends m (1 ≤ m ≤ 1000), whom Dima gave the question. Each of the next 2 * m lines has the next structure: first line contains two numbers n and k (1 ≤ k ≤ n ≤ 10000), second line contains k - 1 numbers - the number of balls of the next known color, written on the plate.

Output

Each of the m lines should contain the answer to Dima's problem, printed with an accuracy of 5 digits after the decimal point.