$\huge\color{cadetblue}{\text{Binary Palindromes}}$
A palindrome is a symmetrical string, that is, a string that reads identically from left to right as well as from right to left. Thus, abcba is a palindrome, but abab is not. In this problem we consider binary palindromes, which are binary strings (sequences of 0s and 1s) that are palindromes. For instance, the following strings are binary palindromes: 101, 11011, 100001.
Given are two non-negative decimal integers $a$ and $b$ ($0 \leq a \leq b < 2147483647$). You have to find all binary palindromes $p$ such that $a \leq p \leq b$ and $p$ has an odd number of 1s. Your program should output these palindromes in ascending order, one per line. Each palindrome should be preceded by its decimal value, a colon and a space. If there are no binary palindromes in the specified interval, your program should output a single line containing the single integer 0. The intervals are chosen such that the output does not exceed 1200 lines.
$\Large\color{darkseagreen}{\text{Example}}$
Input:
Output:
1: 1
7: 111
21: 10101
31: 11111