Look, up in the sky! It's a super duper array! 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 &gt; 2
6 &gt; 3 + 2 (5)
13 &gt; 6 + 3 + 2 (11)


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

3 &gt; 2
5 == 3 + 2
11 &gt; 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 &gt; 2
7 &gt; 3 * 2 (6)
43 &gt; 7 * 3 * 2 (42)
1856 &gt; 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++). Also, you can assume that all of the numbers in the list will be integers greater than 0.
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! It's also possible for an array to be duper-non-super. For example {1, 2, 3} In this case, you should print It's a 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.
Jelly, 47 45 4̷4̷ 42 bytes

+\,×\&lt;ḊZṖP“sd”x;€“uper ”;/“It's a ”,“¥ṫɲ»j


This prints an empty string (falsy) for arrays that are neither super nor duper. Try it online!

How it works

+\,×\&lt;ḊZṖP“sd”x;€“uper ”  Main link (first half). Argument: A (array)

+\                        Compute all partial sums of A.

   ×\                     Compute all partial products of A.
  ,                       Pair the results to the left and to the right.
     &lt;Ḋ                   Perform vectorized comparison with A[1:].
                          This yields a 2D array of Booleans.
       Z                  Zip; pair the Booleans corresponding to each integer.
        Ṗ                 Remove the last pair.
                          (Nothing is compared with the last sum/product.)
         P                Take the product of each column.
          “sd”x           Perform vectorized character repetition.
                          This yields ['s', d'], ['s'], ['d'], or [].
               ;€“uper ”  Append the string "uper " to each character.


;/“It's a ”,“¥ṫɲ»j        Main link (second half).

;/                        Reduce the resulting array of strings by concatenation.
                          This will fail for an empty array, exiting immediately.
  “It's a ”,“¥ṫɲ»         Push ['It's a ', 'array!'].
                 j        Join that array, separating by the super duper string.