Inspired by this question from our rivals friends over at code-review.

#Definitions

A super array is an array where each new element in the array is larger than the sum of all the previous elements. {2, 3, 6, 13} is a super array because

3 > 2
6 > 3 + 2 (5)
13 > 6 + 3 + 2 (11)

{2, 3, 5, 11} is not a super array, because

3 > 2
5 == 3 + 2
11 > 5 + 3 + 2

A duper array is an array where each new element in the array is larger than the product of all the previous elements. {2, 3, 7, 43, 1856} is a super array, but it is also a duper array since

3 > 2
7 > 3 * 2 (6)
43 > 7 * 3 * 2 (42)
1856 > 43 * 7 * 3 * 2 (1806)

#The challenge

Write a function or program that takes an array as input in your languages native list format, and determines how super the array is. You can also optionally take an array length input (for languages like C/C++). If it's a super array, you must print It's a super array! If it is a super duper array, you must print It's a super duper array! If the array is neither super nor duper, you can print a falsy value.

As usual, this is code-golf, so standard loopholes apply, and the shortest answer in bytes wins.