Problem J
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 $7$.
Task
You are supposed to find the $M$-th base-$2$ palindrome and output its base-$10$ representation.
Input
The input is a single line with a single positive integer $M\leq 50\, 000$ in base $10$.
Output
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 |
