We are given N line segments on the 2D plane. We want to find the maximum radius of an empty circle whose center coordinates (xc,yc) are constrained as follows:  0 ≤ xc ≤ L  yc = 0 A circle is empty if no part of a segment is located strictly inside of it (thus, a segment may touch the circle, but may not intersect with the interior of the circle).

The first line of the input file contains the number of test cases T. The test cases are described next. The first line of a test case contains the integer numbers N and L (1 ≤ N ≤ 2000 and 0 ≤ L ≤ 10000). The next N lines of the test case contain 4 integers each, describing the coordinates of the endpoints of a segment: xa, ya, xb and yb. The coordinates of the endpoints of the segment are (xa,ya) and (xb,yb). All the coordinates are between -20000 and +20000. Every two consecutive numbers on the same line are separated by a single blank.

For each test case print a line containing a real number R, denoting the maximum radius of an empty circle whose center obeys the constraints. The number must be printed with 3 decimal digits (the number must be rounded up or down according to the usual rounding rules).

Southeastern European 2010