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

$1 ≤ N ≤ 14$
$1 ≤ X ≤ N$