Robot
The Mars rover "TzTzPetya" roams freely across the Martian surface, transmitting details of its journey back to Earth.
"TzTzPetya" operates using a coordinate system where its starting position is the origin, and the OY axis aligns with the direction it faces upon landing.
The rover's movement pattern is as follows: after landing, it moves forward a whole number of centimeters, ranging from 1 to 10^6. It then turns 90 degrees either left or right, moves forward again within the same range, and turns 90 degrees left or right once more. This sequence continues until it completes its final segment, after which it halts and begins transmitting its journey details back to Earth.
The Control Center received the following message from "TzTzPetya": "I made n movements. Here are the n-1 turns I executed: sequence of turns. I have arrived at the coordinates (x, y). I am content here. End of communication."
At this point, the creators realized they had neglected to program the rover to report the distances it traveled!
They are now eager to determine any possible path "TzTzPetya" could have taken that aligns with the transmitted data. Your task is to assist them.
Input
The first line of input contains three integers x, y, n (-100000 ≤ x, y ≤ 100000; 1 ≤ n ≤ 100000) — representing the final coordinates of "TzTzPetya" and the total number of movements it made.
The second line is a string of length n-1 consisting of the characters "L" and "R" — indicating the sequence of turns made by "TzTzPetya". The character "L" signifies a left turn of 90 degrees, while "R" signifies a right turn of 90 degrees.
Output
If the information is contradictory and the rover could not have moved in such a manner, output "Impossible".
Otherwise, output n integers, each between 1 and 10^6, representing the lengths of "TzTzPetya's" movements in centimeters. These should be consistent with the specified turns, ensuring "TzTzPetya" ends up at the point (x, y). The numbers should be separated by spaces and/or newlines.