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Recursive Integer Multiplication

Write a function `multiply_int(x, y)` that multiplies two integers `x` and `y` using recursion. The function should not use the `*` operator for multiplication but instead rely on repeated addition and subtraction.

#### Example Usage
```python [main.nopy]
print(multiply_int(10, 20))  # Output: 200
print(multiply_int(-5, 10))  # Output: -50
print(multiply_int(4, -8))  # Output: -32
print(multiply_int(0, 5))   # Output: 0
```

#### Constraints
- You may assume that the inputs are valid integers.
def multiply_int(x, y):
    """
    Recursively multiply two integers without using the multiplication operator.

    Args:
        x (int): The first integer.
        y (int): The second integer.

    Returns:
        int: The product of x and y.
    """
    # Base cases and recursive logic to be implemented
    pass
Intermediate recursionfunctions
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