Don`t Burst the Balloon

Input

The input is a sequence of datasets. Each dataset is formatted as follows.

$n$ $w$

x_1 y_1 h_1

...

x_n y_n h_n

The first line of a dataset contains two positive integers, $n$ and $w$, separated by a space. $n$ represents the number of needles, and $w$ represents the height of the side walls.

The bottom of the box is a 100 \times 100 square. The corners of the bottom face are placed at positions ($0$, $0$, $0$), ($0$, $100$, $0$), ($100$, $100$, $0$), and ($100$, $0$, $0$).

Each of the $n$ lines following the first line contains three integers, x_i, y_i, and h_i. (x_i, y_i, $0$) and h_i represent the base position and the height of the $i$-th needle. No two needles stand at the same position.

You can assume that 1 \le n \le 10, 10 \le w \le 200, 0 < x_i < 100, 0 < y_i < 100 and 1 \le h_i \le 200. You can ignore the thicknesses of the needles and the walls.

The end of the input is indicated by a line of two zeros. The number of datasets does not exceed $1000$.

Figure 1. The upper shows an example layout and the lower shows the largest spheric balloon that can be placed.

Output

For each dataset, output a single line containing the maximum radius of a balloon that can touch the bottom of the box without interfering with the side walls or the needles. The output should not contain an error greater than $0.0001$.

Esempi