Problem Statement:

Sami (five years old boy) has a collection of n identical blocks, he is trying to stack them one on top of next one on a table, Sami can stack the blocks in any way he wants. Next figure shows one possible solution to do so. He is trying to arrange the blocks in a way such that one of them hangs out completely over the edge of the table and has the maximum possible offset of it, without having the stack fall over.

From the physic point of view the stable stack is a stack having its mass center relaying on the table (not on air). The mass center of the stack is the center of the mass centers of all the blocks in it and the mass center of a block is the middle point in the block (half way of its width).

Sami tried a lot of times before he gave up and came to you. Your task is to find out the maximum possible offset achievable by building a stack of n blocks each of which has a width of x.

Input Format:

The first line contains one integer 0 < t ≤ 1000 which is the number of test cases. Each test case is a line contains two integers 0 < n ≤ 1000 to denote the number of blocks, and 0 < x ≤ 100 to denote the width of a block.

Output Format:

For each test case you have to output a line contains the maximum achievable offset with a precision of 4 digits. If no offset can be gained you should output the string "impossible".

Sample Input:

3
2 80
10 50
27 22

Sample Output:

impossible
23.2242
20.8060