Flexible FizzBuzz

In the classic game of FizzBuzz, a number divisible by 3 is answered with Fizz, a number divisible by 5 with Buzz, and a number divisible by both with FizzBuzz. You want a configurable version of the game, where the divisors and the words they map to are supplied at run time.

A configuration together with the number to answer is packed into one string called info:

a1:s1,a2:s2,...,am:sm,n

a1 ... am are the divisors, s1 ... sm are the words they map to, and n is the number to answer.

What to return

For a valid info:

if n is divisible by at least one ai, return the word si belonging to the largest such ai;
if no ai divides n, return n itself, written in decimal with no leading zeros.

For an invalid info, return the exact string Invalid Argument.

When is `info` valid?

info is valid only if it is exactly a1:s1,a2:s2,...,am:sm,n with all of the following holding:

1 <= m <= 5.
Every ai is an integer with 1 <= ai <= 100, written in decimal with no leading zeros.
The ai are pairwise distinct.
Every si is non-empty, at most 50 characters long, and made only of the characters 0-9, a-z, A-Z, ? and !.
n is an integer with 1 <= n <= 10000000, written in decimal with no leading zeros.
Exactly one colon separates each ai from its si.
Exactly one comma separates each si from the next a(i+1), and exactly one comma separates sm from n.

Anything else - a missing piece, an extra separator, a stray character, an out-of-range number, a repeated divisor, a leading zero - makes info invalid.

Function Description

Complete the function flexibleFizzbuzz with the following parameter:

string info: one packed configuration-and-number string

### Returns

string: the matching word, or n as a string, or Invalid Argument

Constraints

1 <= t <= 200, where t is the number of queries
Each info is a non-empty string of at most 300 printable ASCII characters and contains no spaces

Input Format

The first line contains a single integer t, the number of queries.

Each of the next t lines contains one string info.

Output Format

Print t lines. Line i is the answer for the i-th info.

Sample Input 0

4
2:fizz,7:buzz,15:mizu,12
8:fizz,12:buzz,18:mizu,14:huga,7:hoge,18
3:Fizz,5:Buzz,4
1:HeyHey,3:d,1000000000000000000000000000000000000

Sample Output 0

fizz
mizu
4
Invalid Argument

### Explanation 0

12 is divisible by 2 only, out of {2, 7, 15}, so the answer is fizz.
Of {8, 12, 18, 14, 7} only 18 divides 18, so the answer is mizu.
4 is divisible by neither 3 nor 5, so the number itself is returned.
n is far above 10000000, so info is invalid.

Sample Input 1

6
2:two,4:four,8:eight,16:sixteen,32:tt,32
2:two,4:four,8:eight,16:sixteen,32:tt,16
2:two,4:four,8:eight,16:sixteen,32:tt,8
2:two,4:four,8:eight,16:sixteen,32:tt,64
2:two,4:four,8:eight,16:sixteen,32:tt,6
32:tt,16:sixteen,8:eight,4:four,2:two,32

Sample Output 1

tt
sixteen
eight
tt
two
tt

### Explanation 1

Several divisors match every time; the largest one always wins, whatever order the pairs are listed in. For n = 6 only 2 divides it, so two is the answer.

Sample Input 2

5
3:x,3:y,9
3:x,5:y,3:z,9
3:x,5:y,9
10:a,10:b,10:c,100
1:a,2:b,3:c,4:d,1:e,12

Sample Output 2

Invalid Argument
Invalid Argument
x
Invalid Argument
Invalid Argument

### Explanation 2

Every query but the third repeats a divisor, and the divisors must be pairwise distinct.