------
## 最终结论
```python
def time_out_of_coverage(t, test_cases):
    results = []
    for a, b, c, r in test_cases:
        if a > b:
            a, b = b, a

        coverage_start = c - r
        coverage_end = c + r

        # Calculate the overlap of Polycarp's path and the coverage area
        overlap_start = max(a, coverage_start)
        overlap_end = min(b, coverage_end)

        # Calculate the time in coverage
        if overlap_start < overlap_end:
            time_in_coverage = overlap_end - overlap_start
        else:
            time_in_coverage = 0

        total_time = b - a
        time_out_of_coverage = total_time - time_in_coverage

        results.append(time_out_of_coverage)

    return results

# Example usage:
t = 9
test_cases = [
    (1, 10, 7, 1),
    (3, 3, 3, 0),
    (8, 2, 10, 4),
    (8, 2, 10, 100),
    (-10, 20, -17, 2),
    (-3, 2, 2, 0),
    (-3, 1, 2, 0),
    (2, 3, 2, 3),
    (-1, 3, -2, 2)
]

print(time_out_of_coverage(t, test_cases))
```