PROBLEM STATEMENT
A string composed of the letters 'A' and 'B' is called beautiful if it satisfies all of the 
following criteria:

it contains no more than countA occurences of 'A';
it contains no more than countB occurences of 'B';
each substring that contains only 'A's consists of no more than maxA characters;
each substring that contains only 'B's consists of no more than maxB characters.

Given countA, countB, maxA and maxB, return the maximum possible length of a beautiful string.

DEFINITION
Class:BeautifulString
Method:maximumLength
Parameters:int, int, int, int
Returns:int
Method signature:int maximumLength(int countA, int countB, int maxA, int maxB)


CONSTRAINTS
-countA will be between 0 and 1000000, inclusive.
-countB will be between 0 and 1000000, inclusive.
-maxA will be between 0 and 1000000, inclusive.
-maxB will be between 0 and 1000000, inclusive.


EXAMPLES

0)
0
0
10
10

Returns: 0

We don't have any available letters as countA=0 and countB=0, so the only beautiful string is the 
empty one.

1)
10
10
0
0

Returns: 0

Now we have available letters, but can't include them into the beautiful string as maxA=0 and 
maxB=0.

2)
3
5
1
1

Returns: 7

In this case we can't have two consecutive 'A's or 'B's, so letters in the beautiful string should 
alternate. If we start the string from 'A', the longest one we'll be able to get is "ABABAB". But 
if we start the string from 'B', we'll be able to get the longer one - "BABABAB".

3)
677578
502524
989951
504698

Returns: 1180102

Here maxA >= countA and maxB >= countB, so we can easily construct a beautiful string using all 
available countA+countB letters.

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 unauthorized use or reproduction of this information without the prior written consent of 
 TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.
 
  This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.