PROBLEM STATEMENT
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In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such 
that the difference of any two successive members of the sequence is a constant. For instance, the 
sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2. An 
arithmetic sequence can always be represented as an=a0+n*d.


You will be given a sequence seq, where seqi = [ai+1] for some nondecreasing arithmetic sequence a 
(both indices are 0-based). [x] denotes the floor function (see Notes). The sequence a is defined 
as a0+i*d. Return the minimal possible value for d. If no possible value exists for d, return -1 
instead.


DEFINITION
Class:ArithmeticProgression
Method:minCommonDifference
Parameters:int, vector <int>
Returns:double
Method signature:double minCommonDifference(int a0, vector <int> seq)


NOTES
-[x] denotes the floor function of x which returns the highest integer less than or equal to x. 
For example, [3.4] = 3, [0.6] = 0, [-1.2] = -2 and [-0.6] = -1.
-Your return value must be accurate to within an absolute or relative tolerance of 1E-9.


CONSTRAINTS
-seq will contain between 0 and 50 elements, inclusive.
-Each element of seq will be between -10^6 and 10^6, inclusive.
-a0 will be between -10^6 and 10^6, inclusive.


EXAMPLES

0)
0
{6, 13, 20, 27}

Returns: 6.75



1)
1
{2, 3, 4, 5, 6}

Returns: 1.0



2)
3
{}

Returns: 0.0

Since the sequence a is nondecreasing, d must be at least 0.

3)
3
{3, 3, 3, 3, 4}

Returns: 0.2



4)
1
{-3}

Returns: -1.0



5)
0
{6, 14}

Returns: -1.0



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