find-the-fishy-number

Pick a random financial transaction from the ledger of a typical business and there is about a 30% chance that the first non-zero digit of the amount of money involved is a 1. This counter-intuitive fact is a result of Benford's Law, discovered by astronomer Simon Newcomb in the late 1800's and rediscovered by physicist Frank Benford in the early 1900's. They found that real world data are not evenly distributed. Instead, given a random number related to some natural or social phenomenon satisfying certain conditions, the probability that the first non-zero digit of the number is D is log10(1 + 1/D).
Increasingly, financial auditors are using Benford's Law to detect possible fraud. Given a record of the financial transactions of a company, if some leading digit appears with a frequency that significantly differs from that predicted by Benford's Law, it is a signal that those transactions deserve a closer look.
Return the smallest digit that appears as the first non-zero digit of numbers in transactions with a frequency that is at least threshold times more or less than its expected frequency (e.g., more than 
three times the expected frequency or less than one-third the expected frequency when threshold=3). If no such digit exists, return -1.

First line contains number of test cases.
In every test case first line contains n (Number of transactions)
Then n space separated integers follows.
Then the threshold value is given.
1 ≤ t ≤ 25
1 ≤ n ≤ 50
1 ≤ elements ≤ 999999999
2 ≤ threshold ≤ 10

SAMPLE INPUT
1
20
5236 7290 200 1907 3336 9182 17 4209 8746 7932 6375 909 2189 3977 2389 2500 1239 3448 6380 4812
2

SAMPLE OUTPUT
1

Explanation

The following chart gives the actual frequency of each leading digit, and its expected frequency according to Benford's law.
    digit    | 1    2    3    4    5    6    7    8    9
    ---------|---------------------------------------------
    actual   | 3    4    3    2    1    2    2    1    2
    expected | 6.02 3.52 2.50 1.94 1.58 1.34 1.16 1.02 0.92
Assuming a threshold of 2, there are two digits that are questionable: the leading digit 1 appears less than half as often as expected and the leading digit 9 appears more than twice as often as expected. Since 1 is smaller than 9, the answer is 1.

Source: hackerearth | Difficulty: EASY


Solutions: