A bridge is B steps long. Each step offers two panels, one safe and one that breaks, and nobody knows which is which. Players cross one at a time, and everything an earlier player discovers stays known to those behind.

Return the probability that player i (1-indexed) survives.

• a player only guesses when they reach a panel nobody has tested
• a wrong guess costs that player, but reveals the panel for good
• so the number of players lost before the bridge is fully mapped is $D \sim \mathrm{Binomial}(B, 1/2)$

Player i survives exactly when $D \leq i - 1$.

Input

B = 18
i = 1

Output

3.814697265625e-06