# Intervals

Source : ACM ICPC Central European Regional 1996 |
|||

Time limit : 3 sec |
Memory limit : 32 M |

**Submitted** : 389, **Accepted** : 146

Within this model, the x-axis has been aligned with the level of the floor. The light is considered to be a point light source with integer co-ordinates [bx,by]. The pipes are represented by circles. The center of the circle i has the integer co-ordinates [cxi,cyi] and an integer radius ri. As pipes are made from solid material, circles cannot overlap. Pipes cannot reflect the light and the light cannot go through the pipes. You have to write a program which will determine the non-overlapping intervals on the x-axis where there is, due to the pipes, no light from the light source.

"""

Input

The input consists of blocks of lines, each of which except the last describes
one situation in the basement. The first line of each block contains a positive
integer number N < 500 expressing the number of pipes. The second line of
the block contains two integers bx and by separated by one space. Each of the
next N lines of the block contains integers cxi, cyi and ri, where cyi + ri
< by. Integers in individual lines are separated by one space. The last block
consists of one line containing n = 0.

**Output**

The output consists of blocks of lines, corresponding to the blocks in the input(except
the last one). One empty line must be put after each block in the output. Each
of the individual lines of the blocks in the output will contain two real numbers,
the endpoints of the interval where there is no light from the given point light
source. The reals are exact to two decimal places and separated by one space.
The intervals are sorted according to increasing x-coordinate.

**Sample Input**

6 300 450 70 50 30 120 20 20 270 40 10 250 85 20 220 30 30 380 100 100 1 300 300 300 150 90 1 300 300 390 150 90 0

Sample Output

0.72 78.86 88.50 133.94 181.04 549.93 75.00 525.00 300.00 862.50