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Check Opposite Signs

Write a Python function `opposite_signs(x, y)` that checks whether two given integers have opposite signs. The function should return `True` if the integers have opposite signs and `False` otherwise.

#### Example Usage
```python [main.nopy]
print(opposite_signs(1, -2))  # Output: True
print(opposite_signs(3, 2))   # Output: False
print(opposite_signs(-10, -10))  # Output: False
print(opposite_signs(-2, 2))  # Output: True
```

#### Constraints
- The function should handle both positive and negative integers.
- Zero is considered to have no sign, so any comparison involving zero should return `False`.
def opposite_signs(x, y):
    """
    Check if two integers have opposite signs.

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

    Returns:
        bool: True if x and y have opposite signs, False otherwise.
    """
    # Implement the logic to check for opposite signs
    pass
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