Base Sums

You are given three integers $n$, $a$, and $b$. Find the smallest integer $m$ greater than $n$ whose digit sum in base $a$ equals its digit sum in base $b$.

The input is a single test case. The first line holds three integers $n$, $a$, and $b$, separated by spaces, with $0 \le n \le 10^{16}$ and $2 \le a < b \le 36$. All three are given in base 10.

Print in base 10, on one line, the smallest integer $m$ greater than $n$ whose digit sum in base $a$ equals its digit sum in base $b$. The value of $m$ can be larger than $10^{16}$.