Reversed Multiples

Computer Science Level 5

Let the reverse of a positive integer $n$ , denoted $R(n),$ be the result when the digits of the number are written backwards; for example, $R(190) = 091,$ or just $91.$

Call a positive integer $n$ brilliant if $n + R(n)$

is a multiple of 13. Let $B$ be the $10000$ th brilliant number. Compute the last three digits of $B.$