For the first assignment, we will look at how Haskell handles big numbers.

***NOTE: YOU MAY NOT CHANGE ANY TYPE SIGNATURES***
***IF YOU DO, YOU WILL GET A ZERO FOR THE ASSIGNMENT***

Consider the following Java program (available in Test.java).

  public class Test {
    public void main(String[] args) {
      System.out.println(999999999999999999999 * 2);
    }
  }

You could easily calculate 999999999999999999999 * 2 with pencil and paper;
Java cannot handle it.

  $ javac Test.java
  Test.java:3: error: integer number too large: 999999999999999999999
      System.out.println(999999999999999999999 * 2);
                         ^
  1 error

With Haskell, there is no problem:

  $ ghci
  GHCi, version 7.6.3: http://www.haskell.org/ghc/  :? for help
  Loading package ghc-prim ... linking ... done.
  Loading package integer-gmp ... linking ... done.
  Loading package base ... linking ... done.
  Prelude> 999999999999999999999 * 2
  1999999999999999999998
  Prelude>

So how does Haskell handle these numbers?
We will implement a simplified BigNum module to understand it better.

In our implementation, a number will be a list of "blocks" of numbers from 0-999,
stored with the least significant "block" first. So 9,073,201 will be
stored as:

  [201,73,9]

Your job is to complete BigNum.hs.  The breakdown of points is as follows:
* 10 points -- Complete bigAdd'
*  5 points -- Complete bigSubtract'
*  3 points -- Complete bigMultiply
*  2 points -- Complete bigPowerOf


Starter code is available on the course website.
The files include:
* BigNum.hs -- You will modify this file (only).
* Calculator.hs -- A (very) simple calculator that relies on your BigNum module.
* test.hs -- A number of test cases that use BigNum.
* input -- A number of cases that Calculator.hs should handle correctly.
* output_EXPECTED -- the expected results of calling (from the command line):
  $runhaskell test.hs
  $runhaskell Calculator.hs < input

Note that negative numbers are not supported, and should raise an error.

Submit BigNum.hs through Canvas.