Integers in Rational Bases

Given relatively prime positive integers $p > q$, any positive integer $n$ can be written uniquely as a linear combination of powers of $(p/q)$ with coefficients ranging from $0$ to $p-1$.

$n = a_0 + a_1(p/q) + a_2(p/q)^2 + \cdots$

For example,

$15 = 2(3/2)^4 + 1(3/2)^3 + 0(3/2)^2 + 1(3/2) + 0$

$15 = 4(7/4)^2 + 1(7/4) + 1$

Write a program that finds the base $(p/q)$ expansion of an integer $n$. Use the characters 0-9, then A-Z, then a-z as digits for the base $(p/q)$ expansion.

Input consists of a single line containing 3 space-separated decimal values. They are the numerator $p$ ($3 \le p \le 62$) of the fractional base, followed by the denominator $q$ ($2 \le q \le p-1$) of the fractional base, followed by the positive integer $n$ to be represented in base $(p/q)$. The values of $p$, $q$, and $n$ are chosen so that $p$ and $q$ are relatively prime, the expansion has at most 40 digits, and $n$ fits in a 32-bit unsigned integer.

Your program should produce a single output line containing a string of digits [0-9,A-Z,a-z] with the most significant digit first.