I'm training code problems, and on this one I am having problems to solve it, can you give me some tips how to solve it please.

The problem is something like this:

Your task is to find the sequence of points on the map that the bomber is expected to travel such that it hits all vital links. A link from A to B is vital when its absence isolates completely A from B. In other words, the only way to go from A to B (or vice versa) is via that link.

Notice that if we destroy for example link (d,e), it becomes impossible to go from d to e,m,l or n in any way. A vital link can be hit at any point that lies in its segment (e.g. a hit close to d is as valid as a hit close to e). Of course, only one hit is enough to neutralize a vital link. Moreover, each bomb affects an exact circle of radius R, i.e., every segment that intersects that circle is considered hit.

Due to enemy counter-attack, the plane may have to retreat at any moment, so the plane should follow, at each moment, to the closest vital link possible, even if in the end the total distance grows larger.

Given all coordinates (the initial position of the plane and the nodes in the map) and the range R, you have to determine the sequence of positions in which the plane has to drop bombs.

This sequence should start (takeoff) and finish (landing) at the initial position. Except for the start and finish, all the other positions have to fall exactly in a segment of the map (i.e. it should correspond to a point in a non-hit vital link segment).

The coordinate system used will be UTM (Universal Transverse Mercator) northing and easting, which basically corresponds to a Euclidian perspective of the world (X=Easting; Y=Northing).

Input

Each input file will start with three floating point numbers indicating the X0 and Y0 coordinates of the airport and the range R. The second line contains an integer, N, indicating the number of nodes in the road network graph. Then, the next N (<10000) lines will each contain a pair of floating point numbers indicating the Xi and Yi coordinates (1

No two links will ever cross with each other.

Output

The program will print the sequence of coordinates (pairs of floating point numbers with exactly one decimal place), each one at a line, in the order that the plane should visit (starting and ending in the airport).

Sample input 1

102.3 553.9 0.2
14
342.2 832.5
596.2 638.5
479.7 991.3
720.4 874.8
744.3 1284.1
1294.6 924.2
1467.5 659.6
1802.6 659.6
1686.2 860.7
1548.6 1111.2
1834.4 1054.8
564.4 1442.8
850.1 1460.5
1294.6 1485.1
17
1 2
1 3
2 4
3 4
4 5
4 6
6 7
7 8
8 9
8 10
9 10
10 11
6 11
5 12
5 13
12 13
13 14

Sample output 1

102.3 553.9
720.4 874.8
850.1 1460.5
102.3 553.9