ST Task

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

  You get a ST task, that is: given a stick one end of who is moored on the ground, you are asked to turn over the stick by holding the other end. When it reaches the ground again, the task is finished. It is true that on the process, the stick is always on the same plane vertical the ground. And on this plane, there is light from up to down, so that we can see on the ground a line of shadow. Look at the picture:
In order to express the shadow part and the un-shadow (light space) part, to simple the problem we just need to express the length that 2 times of the length of the stick where the shadow may occur. 
Now, give the problem: the stick on the beginning is on the left of the moored point, and we turn it on certain angular speed, using a ‘S’ to denote one unit of the light space and a ‘T’ for one unit of the shadow line. Beside that, a real number is needed to tell the scale between the shadow line and the full line where shadow may be.

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Input

  There is only one case. Two integers L (0 < L ≤ 25) and V (0 < V ≤ 90) is given.
L is the length of the stick; V is the angular speed of the turning task, in angle per second

Output

  For every second during the task, you are asked to tell the shape of the shadow on the ground. See the sample: ‘S’ for the light space and ‘T’ for the shadow.

Sample Input

1 51

Sample Output

TS  0.50000
TS  0.31466
SS  0.10396
ST  0.44550

Hint

  If the stick is 3 in length, and the shadow line is 1.49, we have the answer this moment: SSTSSS 0.24833 If the stick is 3 in length, and the shadow line is 1.51, we have the answer this moment: STTSSS 0.25167 That is, the number of ‘T’ always is the nearest integer of the length of shadow.

Source

2009湖南大学校赛