Robot Rotation

AtCoder

IDabc326_f

Time4000ms

Memory256MB

Difficulty—

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. You will perform the following operation for $i=1,\ldots,N$ in this order. * Rotate the robot $90$ degrees clockwise or counterclockwise. Then, the robot moves forward $A_i$ units in the direction it is facing. Can the direction of rotation be chosen so that the robot will be at the coordinates $(X,Y)$ after the $N$ operations? If it is possible, determine which direction, clockwise or counterclockwise, should be chosen for each operation. ## Constraints * $1 \leq N \leq 80$ * $1 \leq A_i \leq 10^7$ * $-10^9\leq X,Y \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $X$ $Y$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3 -2 4
3 2 1

Output #1

Yes
LLR

Initially, 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.

*   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 $(0,3)$.
*   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 $(-2,3)$.
*   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 $(-2,4)$.

![image](https://img.atcoder.jp/abc326/79baf4537d56c0df5c5d254e6e7f9616.png)

Input #2

1 0 0
1

Output #2

No

Input #3

4 0 0
1 1 1 1

Output #3

Yes
LRRR

Outputs such as `LLLL` and `RRRR` are also accepted.

Input #4

14 2543269 -1705099
3 14 159 2653 58979 323846 2643383 2795028 841971 69399 37510 58 20 9

Output #4

Yes
LLLLLLLLLRLRRR

API Response (JSON)

{
  "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.\nY...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments