Sure! Below is a test case generator for the provided problem statement:

```python
import random
import math

def generate_test_case():
    # Constants
    MAX_HAND_LENGTH = 1000
    MAX_HOURS = 11
    MAX_MINUTES = 59
    
    # Generate random values for A, B, H, and M within their respective constraints
    A = random.randint(1, MAX_HAND_LENGTH)
    B = random.randint(1, MAX_HAND_LENGTH)
    H = random.randint(0, MAX_HOURS)
    M = random.randint(0, MAX_MINUTES)
    
    return A, B, H, M

def calculate_distance(A, B, H, M):
    # Calculate angles in degrees
    hour_angle = (H % 12) * 30 + M * 0.5
    minute_angle = M * 6
    
    # Convert angles to radians
    hour_angle_rad = math.radians(hour_angle)
    minute_angle_rad = math.radians(minute_angle)
    
    # Calculate coordinates of the endpoints
    hour_x = A * math.cos(hour_angle_rad)
    hour_y = A * math.sin(hour_angle_rad)
    minute_x = B * math.cos(minute_angle_rad)
    minute_y = B * math.sin(minute_angle_rad)
    
    # Calculate distance between the two endpoints
    distance = math.sqrt((hour_x - minute_x)**2 + (hour_y - minute_y)**2)
    
    return distance

def main():
    # Generate test case
    A, B, H, M = generate_test_case()
    
    # Calculate the distance
    distance = calculate_distance(A, B, H, M)
    
    # Print input and output in the required format
    print(f"Input: {A} {B} {H} {M}")
    print(f"Output: {distance:.20f}")

# Run the main function to generate a test case and its corresponding output
main()
```

This script generates random values for A, B, H, and M within the specified constraints, calculates the distance between the endpoint of the hour and minute hands, and prints both the input and the output. The calculation ensures that the distance is accurate up to the required precision of \(10^{-9}\).