A7945. Collisions

On a number line there are $n$ balls. At time moment $0$ for each ball the following data is known: its coordinate $x_{i}$ , speed $v_{i}$ (possibly, negative) and weight $m_{i}$ . The radius of the balls can be ignored.

The balls collide elastically, i.e. if two balls weighing $m_{1}$ and $m_{2}$ and with speeds $v_{1}$ and $v_{2}$ collide, their new speeds will be:

.Your task is to find out, where each ball will be $t$ seconds after.

The first line contains two integers $n$ and $t$ ( $1<=n<=10,0<=t<=100$ ) — amount of balls and duration of the process. Then follow $n$ lines, each containing three integers: $x_{i}$ , $v_{i}$ , $m_{i}$ ( $1<=|v_{i}|,m_{i}<=100,|x_{i}|<=100$ ) — coordinate, speed and weight of the ball with index $i$ at time moment $0$ .

It is guaranteed that no two balls have the same coordinate initially. Also each collision will be a collision of not more than two balls (that is, three or more balls never collide at the same point in all times from segment $[0;t]$ ).

Output $n$ numbers — coordinates of the balls $t$ seconds after. Output the numbers accurate to at least 4 digits after the decimal point.