{"problem":{"name":"Robot Rotation","description":{"content":"A robot is at the origin of a coordinate plane where the positive $x$\\-axis points to the right and the positive $y$\\-axis points upwards. Initially, the robot is facing the positive $x$\\-direction. Y","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc326_f"},"statements":[{"statement_type":"Markdown","content":"A robot is at the origin of a coordinate plane where the positive $x$\\-axis points to the right and the positive $y$\\-axis points upwards. Initially, the robot is facing the positive $x$\\-direction.\nYou will perform the following operation for $i=1,\\ldots,N$ in this order.\n\n*   Rotate the robot $90$ degrees clockwise or counterclockwise. Then, the robot moves forward $A_i$ units in the direction it is facing.\n\nCan the direction of rotation be chosen so that the robot will be at the coordinates $(X,Y)$ after the $N$ operations?\nIf it is possible, determine which direction, clockwise or counterclockwise, should be chosen for each operation.\n\n## Constraints\n\n*   $1 \\leq N \\leq 80$\n*   $1 \\leq A_i \\leq 10^7$\n*   $-10^9\\leq X,Y \\leq 10^9$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $X$ $Y$\n$A_1$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc326_f","tags":[],"sample_group":[["3 -2 4\n3 2 1","Yes\nLLR\n\nInitially, the robot is at $(0,0)$ and facing the positive $x$\\-direction. The following choices can put the robot at the coordinates $(X,Y)$ after the $N$ operations.\n\n*   First operation: Rotate the robot $90$ degrees counterclockwise to face the positive $y$\\-direction. The robot moves forward $A_1=3$ units in the direction it is facing, and moves to $(0,3)$.\n*   Second operation: Rotate the robot $90$ degrees counterclockwise to face the negative $x$\\-direction. The robot moves forward $A_2=2$ units in the direction it is facing, and moves to $(-2,3)$.\n*   Third operation: Rotate the robot $90$ degrees clockwise to face the positive $y$\\-direction. The robot moves forward $A_3=1$ unit in the direction it is facing, and moves to $(-2,4)$.\n\n![image](https://img.atcoder.jp/abc326/79baf4537d56c0df5c5d254e6e7f9616.png)"],["1 0 0\n1","No"],["4 0 0\n1 1 1 1","Yes\nLRRR\n\nOutputs such as `LLLL` and `RRRR` are also accepted."],["14 2543269 -1705099\n3 14 159 2653 58979 323846 2643383 2795028 841971 69399 37510 58 20 9","Yes\nLLLLLLLLLRLRRR"]],"created_at":"2026-03-03 11:01:14"}}