Two-Wheel Buggy#3309

Two-Wheel Buggy

1 second

256 megabytes

Easy

International Car Production Company (ICPC), one of the largest automobile manufacturers in the world, is now developing a new vehicle called "Two-Wheel Buggy". As its name suggests, the vehicle has only two wheels. Quite simply, "Two-Wheel Buggy" is made up of two wheels (the left wheel and the right wheel) and a axle (a bar connecting two wheels). The figure below shows its basic structure.

Figure 1: The basic structure of the buggy

Before making a prototype of this new vehicle, the company decided to run a computer simulation. The details of the simulation is as follows.

In the simulation, the buggy will move on the x-y plane. Let $D$ be the distance from the center of the axle to the wheels. At the beginning of the simulation, the center of the axle is at $(0, 0)$ , the left wheel is at $(- D, 0)$ (-D, 0), and the right wheel is at $(D, 0)$ . The radii of two wheels are $1$ .

Figure 2: The initial position of the buggy

The movement of the buggy in the simulation is controlled by a sequence of instructions. Each instruction consists of three numbers, $L s p ee d$ , $R s p ee d$ and $t im e$ . $L s p ee d$ and $R s p ee d$ indicate the rotation speed of the left and right wheels, respectively, expressed in degree per second. $t im e$ indicates how many seconds these two wheels keep their rotation speed. If a speed of a wheel is positive, it will rotate in the direction that causes the buggy to move forward. Conversely, if a speed is negative, it will rotate in the opposite direction. For example, if we set $L s p ee d$ as $- 360$ , the left wheel will rotate $360$ -degree in one second in the direction that makes the buggy move backward. We can set $L s p ee d$ and $R s p ee d$ differently, and this makes the buggy turn left or right. Note that we can also set one of them positive and the other negative (in this case, the buggy will spin around).

Figure 3: Examples

Your job is to write a program that calculates the final position of the buggy given a instruction sequence. For simplicity, you can assume that wheels have no width, and that they would never slip.

Input

The input consists of several datasets. Each dataset is formatted as follows.

$N$ $D$ $L s p ee d_{1}$ Lspeed_1 $R s p ee d_{1}$ Rspeed_1 $t im e_{1}$ time_1 ... $L s p ee d_{i}$ Lspeed_i $R s p ee d_{i}$ Rspeed_i $t im e_{i}$ time_i ... $L s p ee d_{N}$ Lspeed_N $R s p ee d_{N}$ Rspeed_N $t im e_{N}$ time_N

The first line of a dataset contains two positive integers, $N$ and $D$ ( $1 \leq N \leq 100$ 1 \le N \le 100, $1 \leq D \leq 10$ 1 \le D \le 10). $N$ indicates the number of instructions in the dataset, and $D$ indicates the distance between the center of axle and the wheels. The following $N$ lines describe the instruction sequence. The $i$ -th line contains three integers, $L s p ee d_{i}$ Lspeed_i, $R s p ee d_{i}$ Rspeed_i, and $t im e_{i}$ time_i ( $- 360 \leq L s p ee d_{i}, R s p ee d_{i} \leq 360$ -360 \le Lspeed_i, Rspeed_i \le 360, $1 \leq t im e_{i}$ 1 \le time_i), describing the $i$ -th instruction to the buggy. You can assume that the sum of $t im e_{i}$ time_i is at most $500$ .

The end of input is indicated by a line containing two zeros. This line is not part of any dataset and hence should not be processed.

Output

For each dataset, output two lines indicating the final position of the center of the axle. The first line should contain the $x$ -coordinate, and the second line should contain the $y$ -coordinate. The absolute error should be less than or equal to $1 0^{- 3}$ 10^{-3}. No extra character should appear in the output.

Examples

Example 1