Moves on Binary Tree

AtCoder

IDabc243_d

Time2000ms

Memory256MB

Difficulty—

There is a perfect binary tree with $2^{10^{100}}-1$ vertices, numbered $1,2,...,2^{10^{100}}-1$. Vertex $1$ is the root. For each $1\leq i < 2^{10^{100}-1}$, Vertex $i$ has two children: Vertex $2i$ to the left and Vertex $2i+1$ to the right. Takahashi starts at Vertex $X$ and performs $N$ moves, represented by a string $S$. The $i$\-th move is as follows. * If the $i$\-th character of $S$ is `U`, go to the parent of the vertex he is on now. * If the $i$\-th character of $S$ is `L`, go to the left child of the vertex he is on now. * If the $i$\-th character of $S$ is `R`, go to the right child of the vertex he is on now. Find the index of the vertex Takahashi will be on after $N$ moves. In the given cases, it is guaranteed that the answer is at most $10^{18}$. ## Constraints * $1 \leq N \leq 10^6$ * $1 \leq X \leq 10^{18}$ * $N$ and $X$ are integers. * $S$ has a length of $N$ and consists of `U`, `L`, and `R`. * When Takahashi is at the root, he never attempts to go to the parent. * When Takahashi is at a leaf, he never attempts to go to a child. * The index of the vertex Takahashi is on after $N$ moves is at most $10^{18}$. ## Input Input is given from Standard Input in the following format: $N$ $X$ $S$ [samples]

Samples

Input #1

3 2
URL

Output #1

6

The perfect binary tree has the following structure.
![image](https://img.atcoder.jp/ghi/9e199e154f481af436c8eaec9c487e2c.png)
In the three moves, Takahashi goes $2 \to 1 \to 3 \to 6$.

Input #2

4 500000000000000000
RRUU

Output #2

500000000000000000

During the process, Takahashi may be at a vertex whose index exceeds $10^{18}$.

Input #3

30 123456789
LRULURLURLULULRURRLRULRRRUURRU

Output #3

126419752371

API Response (JSON)

{
  "problem": {
    "name": "Moves on Binary Tree",
    "description": {
      "content": "There is a perfect binary tree with $2^{10^{100}}-1$ vertices, numbered $1,2,...,2^{10^{100}}-1$.   Vertex $1$ is the root. For each $1\\leq i < 2^{10^{100}-1}$, Vertex $i$ has two children: Vertex $2i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc243_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a perfect binary tree with $2^{10^{100}}-1$ vertices, numbered $1,2,...,2^{10^{100}}-1$.  \nVertex $1$ is the root. For each $1\\leq i < 2^{10^{100}-1}$, Vertex $i$ has two children: Vertex $2i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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