Problem Statement

PROBLEM STATEMENT

When a binary message is transmitted across a network, there is always a chance
that the message might be corrupted by the time it is received.  In order for
the receiver to determine if an error occurred during transmission, the
transmitter sends an additional shorter message, called the key.  The key is
functionally derived from the first message and is used by the receiver to
perform a check based on both of these messages.

Suppose there is an original binary message M, and the derived binary message
key K. The verification check is accomplished by performing a bitwise
operation. Let R be the "residue", which is the result of performing this
bitwise operation on M and K. The bitwise operation is performed as follows:

1. Align K beneath M, starting with the left-most nonzero bit of M. 
2. Execute an XOR operation on M and K where XOR(x,y)=0 (zero) if x is the same
as y, and XOR(x,y)=1 (one) if x is different than y.  Let R equal the result of
this step.
3. Repeat steps 1 and 2 on each newly derived R until |R| is equal to |K|-1. If
|R| is less than |K|-1, left-pad R with 0's (zeros) until the final |R| is
equal to |K|-1.

If the final residue is all zeros, the message was transmitted correctly.
Otherwise, an error occurred.

Create a class BitChecker that contains the method getResidue, which takes two
binary Strings, M and K as input and returns a binary String representing the
final residue. 

DEFINITION
Class: BitChecker
Parameters: String, String
Returns: String
Method signature (be sure your method is public):  String getResidue(String M,
String K);


NOTES
- Assume the key message is always received correctly.
- Let |K| be the length of K.
- Let |M| be the length of M counting from the leftmost nonzero bit to the
right most bit (inclusive).
- Let |R| be the length of R counting from the leftmost nonzero bit to the
right most bit (inclusive).



TopCoder will ensure the validity of the inputs.  Inputs are valid if all of
the following criteria are met:
- The |M| > |K|.
- The leftmost bit in K must be 1.
- Each bit of both M and K can only be a 1 (one) or 0 (zero).
- M can be of length 3 - 50 (inclusive) counting from the leftmost nonzero bit
to the rightmost bit (inclusive).
- K can be of length 2 - 49 (inclusive) counting from the leftmost nonzero bit
to the rightmost bit (inclusive).
	
EXAMPLES
Here's an example, with M = 10011010010011 and K = 10011:

10011010010011
10011
-----
00000010010011
      10011
      -----
00000000001011 
          Method returns 1011 

Here's another example, with M = 11010110111110 and K = 10011:
11010110111110
10011
-----
01001110111110
 10011
 -----
00000010111110
      10011
      -----
00000000100110
        10011
        -----
00000000000000 

Method returns 0000

Definition