The third year is organizing a farewell party for their seniors before they all go for their internships. They decide to book a club for the party. Akhil, being one of the members of the organizing committee, is given the charge to find a club. He goes to one of the clubs and there he finds something fascinating.

He sees a peculiar arrangement of glasses. There is one glass in the top row, two in the second, three in the third and so on. Each glass rests on a similar left and right glass. The capacity of each glass is 1 unit. The glasses are arranged so perfectly that the drink never spills out the arrangement. Overflow takes place in such a way that after 1 unit, 1/2 of the remaining unit gets into the bottom left glass and another half in the bottom right glass. Akhil starts to wonder what if he pours N units of drink into the top glass, he is curious to know how much quantity of drink will be there in the jth glass of ith row. Can you help him find the answer? Assume that there is a sufficient number of glasses, such that the drink never spills out.

Input: First line of the input contains an integer T denoting the number of test cases and each test case consists of three lines. The first line contains an integer N, the second line contains an integer i and third line contains an integer j.

Output: Corresponding to each test case output the remaining amount of water in jth glass of the ith row correct to 6 decimal places.

Constraints:

T<=20 N<=1000 i <= N j<= N