Water Overflow
Medium Accuracy: 33.55% Submissions: 15879 Points: 4

There is a stack of water glasses in a form of pascal triangle and a person wants to pour the water at the topmost glass, but the capacity of each glass is 1 unit. Overflow takes place in such a way that after 1 unit, 1/2 of remaining unit gets into bottom left glass and other half in bottom right glass.Now the pours K units of water in the topmost glass and wants to know how much water is there in the jth glass of the ith row.

Note: Assume that there are enough glasses in the triangle till no glass overflows.

Input:
First line of the input contains an integer T denoting the number of test cases and each test case consists of three lines. First line contain an integer K, 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 cup of the ith row correct to 6 decimal places.

Constraints:
1 <= T<=20
1 <= K <= 1000
1 <= i <= K
1 <= j<= K

Example:
Input:

1

2
1

Output:
1