Base-2 Palindromes

A positive integer $N$
is a *base-$b$
palindrome* if the base-$b$ representation of $N$ (with no leading zeros) is a
palindrome, i.e. reads the same way in either direction.
For instance, $7$ (base
$10$) is a palindrome in
any base greater than or equal to $8$. It is also a palindrome in base
$2$ ($111$) and $6$ ($11$), but not in $3$ ($21$), $4$ ($13$), $5$ ($12$), or $7$ ($10$). The first four
base-$2$ palindromes
(written in base $10$) are
$1$, $3$, $5$, and $7$.

You are supposed to find the $M$-th base-$2$ palindrome and output its base-$10$ representation.

The input is a single line with a single positive integer $M\leq 50\, 000$ in base $10$.

The output for input $M$ should be a single line with the base-$10$ representation of the $M$-th base-$2$ palindrome.

Sample Input 1 | Sample Output 1 |
---|---|

1 |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

3 |
5 |