Two-Wheel Buggy

The car maker International Car Production Company (ICPC) is developing a new vehicle called Two-Wheel Buggy. As the name says, the vehicle has only two wheels. The buggy is made of a left wheel, a right wheel, and an axle, which is a bar joining the two wheels.

Figure 1: The basic structure of the buggy

Before building a prototype, the company decided to run a computer simulation. The rules of the simulation are below.

The buggy moves on the x-y plane. Let $D$ be the distance from the center of the axle to each wheel. When the simulation starts, the center of the axle is at $(0, 0)$, the left wheel is at $(-D, 0)$, the right wheel is at $(D, 0)$, and the buggy faces the positive $y$ direction. Both wheels have radius 1.

Figure 2: The initial position of the buggy

A sequence of instructions controls the movement of the buggy. One instruction is three numbers, $Lspeed$, $Rspeed$, and $time$. $Lspeed$ and $Rspeed$ are the rotation speeds of the left wheel and the right wheel in degrees per second, and $time$ is how many seconds the two wheels keep those speeds. A positive speed turns a wheel in the direction that drives the buggy forward, and a negative speed turns it the other way. For example, with $Lspeed$ set to $-360$, the left wheel makes one full turn per second in the direction that drives the buggy backward. You can set $Lspeed$ and $Rspeed$ to different values, and the buggy then turns left or right. You can also set one of them positive and the other negative. The buggy then spins around.

Figure 3: Examples of movement

Write a program that computes the final position of the buggy for a given instruction sequence. Assume the wheels have no width and never slip.

The input holds several datasets. Each dataset has the form below.

N D
Lspeed_1 Rspeed_1 time_1
...
Lspeed_N Rspeed_N time_N

The first line of a dataset holds two positive integers $N$ and $D$ ($1 \le N \le 100$, $1 \le D \le 10$). $N$ is the number of instructions, and $D$ is the distance from the center of the axle to each wheel. Each of the next $N$ lines holds three integers $Lspeed_i$, $Rspeed_i$, and $time_i$ ($-360 \le Lspeed_i, Rspeed_i \le 360$, $1 \le time_i$) describing the $i$-th instruction. The sum of $time_i$ within one dataset is at most 500.

A line holding two zeros marks the end of the input. That line is not a dataset, so do not process it.

For each dataset, print the final position of the center of the axle on two lines. Print the x-coordinate on the first line and the y-coordinate on the second line. Round both coordinates to exactly five digits after the decimal point. When a rounded coordinate is zero, print 0.00000 and not -0.00000. Print no other characters.