public static List<Integer> missingNumbers(List<Integer> arr, List<Integer> brr) {
        //goal: determine which elements in brr are missing or underrepresented in arr
        
        //use a freq map for each val in brr and arr
        Map<Integer, Integer> brrFreqMap = 
            brr.stream()
            .collect(Collectors.
            groupingBy(Function.identity(), Collectors.collectingAndThen(Collectors.counting(), Long::intValue)));
        Map<Integer, Integer> arrFreqMap = 
            arr.stream()
            .collect(Collectors.
            groupingBy(Function.identity(), Collectors.collectingAndThen(Collectors.counting(), Long::intValue)));
        
        //iterate over each key in arr and check if its in brr
        Set<Integer> missingNumbersSet = new HashSet<>();
        for (Map.Entry<Integer, Integer> entry : brrFreqMap.entrySet()) {
            int key = entry.getKey();
            int freqInBrr = entry.getValue();
            int freqInArr = arrFreqMap.getOrDefault(key, 0); // avoids null issues

            if (freqInArr < freqInBrr) {
                missingNumbersSet.add(key);
            }
        }

        // Step 3: Convert to list and sort
        List<Integer> missingNumbers = new ArrayList<>(missingNumbersSet);
        Collections.sort(missingNumbers);
        return missingNumbers;
    }