Sure! Here is a test case generator for the problem statement "Largest Rectangle":

```python
import random

def tcgen():
    H = random.randint(1, 1400)
    W = random.randint(1, 1400)
    
    matrix = []
    for _ in range(H):
        row = [random.randint(0, 1) for _ in range(W)]
        matrix.append(row)
    
    return H, W, matrix

def format_input(H, W, matrix):
    input_str = f"{H} {W}\n"
    for row in matrix:
        input_str += " ".join(map(str, row)) + "\n"
    return input_str.strip()

# Example usage:
H, W, matrix = tcgen()
print(format_input(H, W, matrix))
```

### Explanation:

1. **Function `tcgen`:**
   - It generates random values for `H` and `W` within the range `[1, 1400]`.
   - It creates a matrix of size `H x W` where each element is either `0` or `1`.
   
2. **Function `format_input`:**
   - It formats the generated test case to match the input format provided in the problem statement.

### Example Output:

Running the example usage code will produce an output similar to this:

```
3 4
0 1 0 1
1 0 0 0
0 1 1 1
```

This output represents a valid input case for the "Largest Rectangle" problem, with a matrix of size `3 x 4` filled with random `0`s and `1`s.