Cleaning Robot

AtCoder

IDabc219_f

Time2000ms

Memory256MB

Difficulty—

There is a cleaning robot on the square $(0, 0)$ in an infinite two-dimensional grid. The robot will be given a program represented as a string consisting of four kind of characters `L`, `R`, `U`, `D`. It will read the characters in the program from left to right and perform the following action for each character read. 1. Let $(x, y)$ be the square where the robot is currently on. 2. Make the following move according to the character read: * if `L` is read: go to $(x-1, y)$. * if `R` is read: go to $(x+1, y)$. * if `U` is read: go to $(x, y-1)$. * if `D` is read: go to $(x, y+1)$. You are given a string $S$ consisting of `L`, `R`, `U`, `D`. The program that will be executed by the robot is the concatenation of $K$ copies of $S$. Squares visited by the robot at least once, including the initial position $(0, 0)$, will be cleaned. Print the number of squares that will be cleaned at the end of the execution of the program. ## Constraints * $S$ is a string of length between $1$ and $2 \times 10^5$ (inclusive) consisting of `L`, `R`, `U`, `D`. * $1 \leq K \leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $S$ $K$ [samples]

Samples

Input #1

RDRUL
2

Output #1

7

The robot will execute the program `RDRULRDRUL`. It will start on $(0, 0)$ and travel as follows:  
$(0, 0) \rightarrow (1, 0) \rightarrow (1, 1) \rightarrow (2, 1) \rightarrow (2, 0) \rightarrow (1, 0) \rightarrow (2, 0) \rightarrow (2, 1) \rightarrow (3, 1) \rightarrow (3, 0) \rightarrow (2, 0)$.  
In the end, seven squares will get cleaned: $(0, 0), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)$.

Input #2

LR
1000000000000

Output #2

Input #3

UUURRDDDRRRUUUURDLLUURRRDDDDDDLLLLLLU
31415926535

Output #3

219911485785

API Response (JSON)

{
  "problem": {
    "name": "Cleaning Robot",
    "description": {
      "content": "There is a cleaning robot on the square $(0, 0)$ in an infinite two-dimensional grid. The robot will be given a program represented as a string consisting of four kind of characters `L`, `R`, `U`, `D`",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc219_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a cleaning robot on the square $(0, 0)$ in an infinite two-dimensional grid.\nThe robot will be given a program represented as a string consisting of four kind of characters `L`, `R`, `U`, `D`...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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