PROBLEM STATEMENT
Given a positive integer N, let P(N) denote the product of all digits in the decimal 
representation of N. For example, P(4256) = 4 * 2 * 5 * 6 = 240, P(2112) = 2 * 1 * 1 * 2 = 4 and 
P(100) = 1 * 0 * 0 = 0.

Consider the infinite sequence S = (P(1), P(2), P(3), ...). Given a vector <int> prod containing 
exactly M elements, find the first occurrence of (prod[0], prod[1], ..., prod[M-1]) in S as a 
consecutive subsequence. In other words, return the smallest positive index X such that P(X + i) = 
prod[i] for all i between 0 and M-1, inclusive. The constraints will guarantee that at least one 
such X exists.

DEFINITION
Class:ProductsOfDigits
Method:firstOccurrence
Parameters:vector <int>
Returns:long long
Method signature:long long firstOccurrence(vector <int> prod)


NOTES
-It can be shown that under the constraints of this problem, the return value will always fit 
within a 64-bit signed integer datatype.


CONSTRAINTS
-prod will contain between 1 and 50 elements, inclusive.
-Each element of prod will be between 0 and 1,000,000,000, inclusive.
-There will be at least one occurrence of (prod[0], ..., prod[M-1]) in S as a consecutive 
subsequence, where M is the number of elements in prod.


EXAMPLES

0)
{1, 2, 3, 4, 5}

Returns: 1

Since P(1) = 1, P(2) = 2, ..., P(5) = 5, we have that S starts with an occurrence of (1, 2, 3, 4, 
5).

1)
{9, 0, 1}

Returns: 9

P(9) = 9, P(10) = 0, P(11) = 1.

2)
{0, 0, 0, 0}

Returns: 100

All numbers between 100 and 103, inclusive, have a 0 in their decimal representations.

3)
{288}

Returns: 489

4 * 8 * 9 = 288.

4)
{108864, 127008, 145152, 163296, 0, 22680, 45360, 68040, 90720}

Returns: 789946



5)
{1}

Returns: 1



6)
{0, 1, 2, 3, 4, 5}

Returns: 10



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