You are playing a game with \(N\) cards that are marked from \(1\) to \(N\). The rules of the game are as follows:

• In each turn, you remove some cards. The game goes on until only one card is left.
• If the number of cards that are left is odd, then preserve the card with the smallest number and randomly remove half of the remaining available cards.
• If the number of cards that are left is even, then randomly remove half of the available cards.

Write a program to determine the probability that the \(X^{th}\) card is the last one remaining.

Input format

The first and only line contains two space-separated integers \(N\) and \(X\)

Output format

Print the probability of the \( X^{th}\) card being the last-remaining card in the game.

Constraints

\(1 ≤ N ≤ 14\)
\(1 ≤ X ≤ N\)