It is sometimes desirable to be able to handle numbers of arbitrary size, without having to consider the limit of the machine representation or to rely on a utility library.

A linked list, implemented with pointers and dynamic memory allocation, is a natural solution: we obtain storage to hold digits only when necessary. Such an approach is called infinite precision arithmetic. 

To represent a large number such as 15,000,701,800,029 with a linked list, we could simply create a node for each digit. However, to make more efficient use of memory, we store an integer between 0 and 999 in each node, which gives the effect of base 1, 000 numbers. For example, the number above can be represented by a five-node list (15, 0, 701, 800 and 29).


Your input should contain several pairs of large numbers. Your program should read and echo each pair of numbers, compute and report their sum and product, and go on to process the next pair until the end of input.

Put your solution in the form of a class named LargeNumbers, which uses the Node class to provide nodes for the linked list representation. There should be, among other things, 

- a method to read/get the input from file/keyboard
- a method to put a large number into a linked list
- a method to add two large numbers
- a method to multiply two large numbers
- a method to output a large number

The main method must look like this pseudo-code: 

While (not end of input)

{
Get/Read and echo a pair of numbers N1 and N2;
Output sum (N1, N2);
Output product (N1, N2);
}

So here's a sample output:

Large Number1: 1 506 033 005 018 000 029
Large Number 2: 1 992
Sum is: 1,506,033,005,018,002,021
Product is: 3,000,017,745,995,856,057,768 



Test on a few pairs of large numbers.