In the Common Sum problem, we are given two arrays A and B of length n containing non-negative (not necessarily distinct) integers, and we must determine whether there are indices i1,i2,j1,j2 {1,2,3.n} for which

A[i1] +A[i2] =B[j1] +B[j2]

Design an algorithm that solves the Common Sum problem and has time complexity O(n2logn) in the setting where operations on individual integers take constant time. Your solution must include a description of the algorithm in words, the pseudocode for the algorithm, a justification of its correctness, and an analysis of its time complexity in big- notation.