Strings of Eternity

AtCoder

IDabc135_f

Time2000ms

Memory256MB

Difficulty—

Given are two strings $s$ and $t$ consisting of lowercase English letters. Determine if the number of non-negative integers $i$ satisfying the following condition is finite, and find the maximum value of such $i$ if the number is finite. * There exists a non-negative integer $j$ such that the concatenation of $i$ copies of $t$ is a substring of the concatenation of $j$ copies of $s$. ## Constraints * $1 \leq |s| \leq 5 \times 10^5$ * $1 \leq |t| \leq 5 \times 10^5$ * $s$ and $t$ consist of lowercase English letters. ## Input Input is given from Standard Input in the following format: $s$ $t$ [samples] ## Notes * A string $a$ is a substring of another string $b$ if and only if there exists an integer $x$ $(0 \leq x \leq |b| - |a|)$ such that, for any $y$ $(1 \leq y \leq |a|)$, $a_y = b_{x+y}$ holds. * We assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings $s$ and $t$, $i = 0$ satisfies the condition in the problem statement.

Samples

Input #1

abcabab
ab

Output #1

3

The concatenation of three copies of $t$, `ababab`, is a substring of the concatenation of two copies of $s$, `abcabababcabab`, so $i = 3$ satisfies the condition.
On the other hand, the concatenation of four copies of $t$, `abababab`, is not a substring of the concatenation of any number of copies of $s$, so $i = 4$ does not satisfy the condition.
Similarly, any integer greater than $4$ does not satisfy the condition, either. Thus, the number of non-negative integers $i$ satisfying the condition is finite, and the maximum value of such $i$ is $3$.

Input #2

aa
aaaaaaa

Output #2

\-1

For any non-negative integer $i$, the concatenation of $i$ copies of $t$ is a substring of the concatenation of $4i$ copies of $s$. Thus, there are infinitely many non-negative integers $i$ that satisfy the condition.

Input #3

aba
baaab

Output #3

0

As stated in Notes, $i = 0$ always satisfies the condition.

API Response (JSON)

{
  "problem": {
    "name": "Strings of Eternity",
    "description": {
      "content": "Given are two strings $s$ and $t$ consisting of lowercase English letters. Determine if the number of non-negative integers $i$ satisfying the following condition is finite, and find the maximum value",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc135_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are two strings $s$ and $t$ consisting of lowercase English letters. Determine if the number of non-negative integers $i$ satisfying the following condition is finite, and find the maximum value...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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