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.

Input

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

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