Coin Toss

Sanvi is playing with a coin in which number 1 is written on the top side and number 0 is written at the bottom side. She is planning to toss the coin exactly $N$ times. What is the probability that summation of coin tosses will either be A or B? Your task is to help her find the answer.

Input

Input starts with an integer $T$ ($1≤T≤100000$) denoting the total number of test-cases. Every test-case starts with $N$ ($1 ≤ N ≤ 30$), denoting the total number of times coin is tossed. This is followed by a single line containing two different non-negative integer numbers having value at most $N$, separated by a single space, denoting $A$ and $B$ respectively. ($A \ne B$, $0 \le A, B \le N$)

Output

For every case of input, output the answer in a single line denoting the answer as described in the problem statement. Error less than $10^{-6}$ will be ignored.

Sample

Input	Output
2 1 0 1 2 2 1	1.000000 0.750000