Prefix Concatenation

AtCoder

IDabc257_g

Time2000ms

Memory256MB

Difficulty—

You are given two strings $S$ and $T$ consisting of lowercase English letters. Find the minimum positive integer $k$ such that you can choose (not necessarily distinct) $k$ prefixes of $S$ so that their concatenation coincides with $T$. In other words, find the minimum positive integer $k$ such that there exists a $k$\-tuple $(a_1,a_2,\ldots, a_k)$ of integers between $1$ and $|S|$ such that $T=S_{a_1}+S_{a_2}+\cdots +S_{a_k}$, where $S_i$ denotes the substring of $S$ from the $1$\-st through the $i$\-th characters and $+$ denotes the concatenation of strings. If it is impossible to make it coincide with $T$, print $-1$ instead. ## Constraints * $1 \leq |S| \leq 5\times 10^5$ * $1 \leq |T| \leq 5\times 10^5$ * $S$ and $T$ are strings consisting of lowercase English letters. ## Input Input is given from Standard Input in the following format: $S$ $T$ [samples]

Samples

Input #1

aba
ababaab

Output #1

3

$T=$ `ababaab` can be written as `ab` + `aba` + `ab`, of which `ab` and `aba` are prefixes of $S=$ `aba`.  
Since it is unable to express `ababaab` with two or less prefixes of `aba`, print $3$.

Input #2

atcoder
ac

Output #2

\-1

Since it is impossible to express $T$ as a concatenation of prefixes of $S$, print $-1$.

API Response (JSON)

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  "problem": {
    "name": "Prefix Concatenation",
    "description": {
      "content": "You are given two strings $S$ and $T$ consisting of lowercase English letters. Find the minimum positive integer $k$ such that you can choose (not necessarily distinct) $k$ prefixes of $S$ so that the",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc257_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given two strings $S$ and $T$ consisting of lowercase English letters.\nFind the minimum positive integer $k$ such that you can choose (not necessarily distinct) $k$ prefixes of $S$ so that the...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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