Go around a Circle

AtCoder

IDagc033_e

Time2000ms

Memory256MB

Difficulty—

Consider a circle whose perimeter is divided by $N$ points into $N$ arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to _generate a string $S$ from every point_ when the following condition is satisfied: * We will arbitrarily choose one of the $N$ points on the perimeter and place a piece on it. * Then, we will perform the following move $M$ times: move the piece clockwise or counter-clockwise to an adjacent point. * Here, whatever point we choose initially, it is always possible to move the piece so that the color of the $i$\-th arc the piece goes along is $S_i$, by properly deciding the directions of the moves. Assume that, if $S_i$ is `R`, it represents red; if $S_i$ is `B`, it represents blue. Note that the directions of the moves can be decided separately for each choice of the initial point. You are given a string $S$ of length $M$ consisting of `R` and `B`. Out of the $2^N$ ways to paint each of the arcs red or blue in a circle whose perimeter is divided into $N$ arcs of equal length, find the number of ways resulting in a circle that generates $S$ from every point, modulo $10^9+7$. Note that the rotations of the same coloring are also distinguished. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $|S|=M$ * $S_i$ is `R` or `B`. ## Input Input is given from Standard Input in the following format: $N$ $M$ $S$ [samples]

Samples

Input #1

4 7
RBRRBRR

Output #1

2

The condition is satisfied only if the arcs are alternately painted red and blue, so the answer here is $2$.

Input #2

3 3
BBB

Output #2

Input #3

12 10
RRRRBRRRRB

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Go around a Circle",
    "description": {
      "content": "Consider a circle whose perimeter is divided by $N$ points into $N$ arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to _generate a string $S$ from every point_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc033_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider a circle whose perimeter is divided by $N$ points into $N$ arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to _generate a string $S$ from every point_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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