------
## 最终结论
```python
def find_least_num_of_unique_integers(arr, k):
    from collections import Counter
    
    # Step 1: Count occurrences of each integer
    occurrences = Counter(arr)
    
    # Step 2: Sort by occurrences
    sorted_occurrences = sorted(occurrences.items(), key=lambda x: x[1])
    
    # Step 3: Remove k elements
    unique_count = len(sorted_occurrences)
    
    for num, count in sorted_occurrences:
        if k >= count:
            k -= count
            unique_count -= 1
        else:
            break
            
    return unique_count

# Example usage
arr1 = [5, 5, 4]
k1 = 1
print(find_least_num_of_unique_integers(arr1, k1))  # Output: 1

arr2 = [4, 3, 1, 1, 3, 3, 2]
k2 = 3
print(find_least_num_of_unique_integers(arr2, k2))  # Output: 2
```