Practice on Toph

Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.

Coin Toss

By Bishal_G, khatribiru · Limits 1s, 512 MB

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!=B, 0<=A,B<=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.

Samples

InputOutput
2
1
0 1
2
2 1
1.000000
0.750000

Discussion
Submit

Login to submit