Multiplication by Self-Modification
CJam, 9 8 bytes

A: 1
B: 0
C:  r,(#0q


Try it online in the CJam interpreter.

How it works

(ABcode) e# Push the integer 10 ** len(Bcode).
&lt;SP&gt;     e# Noop. Separates (AB) and C for input reading.
r        e# Read the first whitespace-separated token from STDIN (ABinput).
,(       e# Push the string length minus 1: len(Binput)
#        e# Power operator: 10 ** len(Bcode) len(Binput) # -&gt;
         e#   (10 ** len(Bcode)) ** len(Binput) = 10 ** (len(Bcode) * len(Binput))
0        e# Push an additional 0 to complete len(Bcode) * len(Binput) + 1 zeroes.
q        e# Read the remaining input (C).