Blackflopper inc™️ have begun a new space exploratory program! Their first unit, the Spadunk-00, has now reached orbit around a planet.

Spadunk-00's onboard data transformation system represents its current position in terms of the planet. In other words, the planet will be the origin of a coordinate system, and Spadunk-00's position can be represented as a 2-d coordinate ~(x, y)~.

Spadunk-00 works in a peculiar way. The engineers send a series of commands, all of which either adds a line to the onboard program in Spadunk-00, or executes the program. Prior to the first command issued, the program on Spadunk-00 is empty. Each command can be one of three types:

move(x, y) - adds an instruction to the onboard program. When Spadunk-00 runs the program (which occurs when it runs the execute() command), the instruction this command adds moves Spadunk-00 by ~(x, y)~

blast(v) - adds an instruction to the onboard program. When Spadunk-00 runs the program (which occurs when it runs the execute() command), the instruction this command adds blasts Spadunk-00 away from or towards the planet, so that it is now ~v~ times as far from the planet (which is the origin). In other words, it multiplies both the x coordinate and y coordinate by ~v~.

Note that move(x, y) and blast(v), by themselves, do nothing. However, they add an instruction to Spadunk-00's program, which, when run through the execute() method, would update its position.

execute() - runs the program, executing each instruction which was stored in Spadunk-00 through the move() and blast() commands. The program is run sequentially, running each instruction starting from the earliest added to the latest, thus updating the position of Spadunk-00. All of the lines that were previously on Spadunk-00's program will remain in the program.

Unfortunately, the engineers soon realized that the whiteflipper nation have intercepted their signal and provided Spadunk-00 with ~M~ commands already! Can you, Spock, find out the final coordinates of the Spadunk-00?

Constraints

In all subtasks,

~0\le M\le 2\cdot10^5~.

At any point in time, the absolute value of Spadunk-00's x coordinate and y coordinate will not exceed ~10^9~.

~v\ge 0~

Subtask 1 [10%]

~M\le10^3~.

Subtask 2 [30%]

~Y=y=0~. In other words, at any point in time, Spadunk-00's y-coordinate will be 0.

Subtask 3 [60%]

No additional constraints.

Input Specification

The first line contains two decimals, ~X~ and ~Y~, representing the current coordinates of Spadunk-00.

The second line contains a nonnegative integer, ~M~, representing the number of commands that the Whiteflipper nation sent to Spadunk-00.

The next ~M~ lines are in one of the following formats:

1 x y - the whiteflipper nation sends the move(x, y) command to Spadunk-00. ~x~ and ~y~ are decimals with absolute values less than ~10^9~.

2 v - the whiteflipper nation sends the blast(v) command to Spadunk-00. ~v~ is a decimal with absolute value less than ~10^9~.

3 - the whiteflipper nation sends the execute() command to Spadunk-00.

Output Specification

Two decimals on one line, the x and y coordinate of Spadunk-00 after it runs all of the commands. Only when printing the final answer, round the x and y coordinates to the nearest hundredth, printing out two digits after the decimal point. It is recommended to use double instead of float due to precision differences.

Sample Input

3.0 4.0
6
1 2.0 3.0
2 2.0
3
1 -2.0 5.0
2 0.5
3

Sample Output

11.00 19.50

Sample Explanation

After the first and second commands, the program is:

move(2.0, 3.0)

blast(2.0)

The third command executes this program, the coordinates are updated as such:

move(2.0, 3.0): ~(3.0,4.0)~ -> ~(3.0+2.0, 4.0+3.0)=(5.0, 7.0)~

blast(2.0): ~(5.0, 7.0)~ -> ~(5.0\cdot2.0, 7.0\cdot2.0)=(10.0, 14.0)~

The fourth and fifth command add two more commands. Now, our program is:

move(2.0, 3.0)

blast(2.0)

move(-2.0, 5.0)

blast(0.5)

The final command executes the program once more. The coordinates are updated as such:

move(2.0, 3.0): ~(10.0, 14.0)~ -> ~(12.0, 17.0)~

blast(2.0): ~(12.0, 17.0)~ -> ~(24.0, 34.0)~

move(-2.0, 5.0): ~(24.0, 34.0)~ -> ~(22.0, 39.0)~

blast(0.5): ~(22.0, 39.0)~ -> ~(11.0, 19.5)~

Thus, our final coordinate is ~(11, 19.5)~. When printing your final answer, remember to round to the nearest hundredth and print out two decimal places. Thus, we print out 11.00 19.50