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E. Collisions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOn 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.

Examples

Input

2 9

3 4 5

0 7 8

Output

68.538461538

44.538461538

Input

3 10

1 2 3

4 -5 6

7 -8 9

Output

-93.666666667

-74.666666667

-15.666666667

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