A vector a containing n elements is said to majorize or dominate a vector b with n elements iff for all values k such that 1 ≤ k ≤ n, the sum of the first element of a↓ through the kth element of a↓ is greater than or equal to the sum of the first through kth elements of b↓, where v↓ represents the vector v sorted in descending order.
a_1 >= b_1 a_1 + a_2 >= b_1 + b_2 a_1 + a_2 + a_3 >= b_1 + b_2 + b_3 ... a_1 + a_2 + ... + a_n-1 >= b_1 + b_2 + ... + b_n-1 a_1 + a_2 + ... + a_n-1 + a_n >= b_1 + b_2 + ... + b_n-1 + b_n
where a and b are sorted in descending order.
For the purpose of this challenge, we will be using a slight generalization of majorization: we will say a list is an unsorted majorization of another if all of the above inequalities are true without sorting a and b. (This is, of course, mathematically useless, but makes the challenge more interesting.)
Given an input of two distinct lists a and b of integers in the range 0 through 255 (inclusive), both lists of length n ≥ 1, output whether the first list unsorted-majorizes the second (a > b), the second unsorted-majorizes the first (b > a), or neither.
You may optionally require the length of the two lists to be provided as input. The output must always be one of three distinct values, but the values themselves may be whatever you want (please specify which values represent a > b, b > a, and neither in your answer).
Test cases for a > b:
  [3,2,1] [3,1,2] [6,1,5,2,7] [2,5,4,3,7]
Test cases for b > a:
[9,1] [10,0] [6,5,4] [7,6,5] [0,1,1,2,1,2] [0,1,2,1,2,1]
Test cases for no majorization:
[200,100] [150,250] [3,1,4] [2,3,3] [9,9,9,9,9,0] [8,8,8,8,8,9]