Largest Empty Circle on a Segment

Input

The first line contains the number of test cases $T$. Each test case description follows. The first line of each test case contains the integers $N$ and $L$ (1 \leq N \leq 2000, 0 \leq L \leq 10000). The next $N$ lines each contain $4$ integers: $xa$, $ya$, $xb$, $yb$, representing the endpoints (xa, ya) and (xb, yb) of a segment. All coordinates are in the range $-20000$ to $20000$. Each two consecutive numbers on the same line are separated by a single space.

Output

For each test case, print on a separate line a real number $R$ — the maximum possible radius of an empty circle whose center satisfies the given restrictions. Print the radius with $3$ decimal digits (use standard rounding rules).

Examples