Two Ping Pong players agree to play several games. The players are evenly matched. However, the person serving first has a probability p of winning that game. A serves the first game and thereafter the loser serves first. What is the Probability that A wins the nth game?

Input

Number of test cases T followed by T lines of 'n' - the number of games played; and 'p' probability of person serving first winning.
0 < T < 100

Output

Print for each test case the probability of A winning.
Please print a double value.

Example

Input:
2
4 0.7
7 0.7

Output:
0.4872
0.500819