You will be writing a replacement for Java's `BigInteger` to perform multiplications and to run the extended Euclidean algorithm on integers values that would overflow `long`.
## Specifications:
1. You are provided with the start of a class to process arbitrarily sized integers called `HeftyInteger`. `HeftyInteger`s are represented internally as [two's-complement](https://en.wikipedia.org/wiki/Two%27s_complement) _raw integers_ using byte arrays (i.e., instances of `byte[]`).
1. Currently, `HeftyInteger` has the following operations implemented:
* A constructor that creates a new `HeftyInteger` based off of a provided `byte[]`.
* A method to compute the sum of two `HeftyInteger`s.
* A method to determine the negation of a `HeftyInteger`.
* A method to compute the difference of two `HeftyInteger`s.
* Several other helper methods.
1. Due to the use of a two's complement representation of the integers, positive `HeftyInteger`s should always have at least one leading 0 bit (indicating that the integer is positive) in their `byte[]` representation. This property may cause the array to be bigger than expected (e.g., a 1024-bit positive integer will be represented using a length 129 byte array).
1. `HeftyInteger`s are also be represented using a _big-endian_ byte-order, so the most significant byte is at the 0<supth</sup index of the `byte[]`.
1. You will need to implement the following functions:
* `HeftyInteger multiply(HeftyInteger other)`
* `HeftyInteger[] XGCD(HeftyInteger other)`
* Any additional helper functions that you deem necessary.
1. You may *not* use any calls the Java API class `java.math.BigInteger`, or any other JCL class within `HeftyInteger`.
1. Once `HeftyInteger` is complete, make sure your implementation of `HeftyInteger` can be used to run the driver programs contained in `MultiplicationTest.java` and `XgcdTest.java`. To get full credit, your implementation should be efficient enough to complete multiplication or XGCD given 200-digit inputs within 3 minutes.
