Given a number $a$, consider the set $S(a) =$ {$a^i : i>=0$ } . You create a sorted sequence G formed by taking any number of distinct elements of the set $S(a)$ and adding them. Let the k^th smallest number which can be constructed using this for a given $a$ be denoted as $(a,k)$.

Find the answer for $(a,k) = (13,423732713)$, submit your answer $modulo$ $4222236787$

The elements of the sequence G go as follows ${1, 13, 14, 169, 170, 182, 183 ...}$