CF34E.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.

数轴上有 $n$ 个球。在时刻 $0$，每个球的以下信息已知：其坐标 $x_i$、速度 $v_i$（可能为负）以及质量 $m_i$。球的半径可忽略不计。

球之间发生完全弹性碰撞，即若两个质量分别为 $m_1$ 和 $m_2$、速度分别为 $v_1$ 和 $v_2$ 的球发生碰撞，则碰撞后它们的速度变为：

你的任务是求出 $t$ 秒后每个球的位置。

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]).

第一行包含两个整数 $n$ 和 $t$（$1 \leq n \leq 10$，$0 \leq t \leq 100$）—— 分别表示小球的数量和过程持续时间。接下来是 $n$ 行，每行包含三个整数：$x_i$、$v_i$、$m_i$（$1 \leq |v_i|, m_i \leq 100$，$|x_i| \leq 100$）—— 表示编号为 $i$ 的小球在初始时刻（$t = 0$）的坐标、速度和质量。

保证初始时刻任意两个小球的坐标均不相同。此外，在整个时间段 $[0, t]$ 内，每次碰撞至多涉及两个小球（即不会出现三个或更多小球在同一时刻、同一位置发生碰撞的情况）。

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

输出 $n$ 个数字——即 $t$ 秒后各球的坐标。输出的数字小数点后至少保留 4 位有效数字。