Bit-Pair Sum Combinations

You are given two lists of integers. Your task is to count how many unique combinations of pairs (one from each list) yield the same result when their bits are summed (using bitwise addition, not normal addition). Return the count of unique sums generated. Example: Input: 3 1 2 3 4 4 5 6 Output: 6 Explanation: Each pair (x from first list, y from second) gives a unique sum based on bitwise operations, resulting in 6 unique values.