Two Abbreviations

AtCoder

IDagc028_a

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ and another string $T$ of length $M$. These strings consist of lowercase English letters. A string $X$ is called a **good string** when the following conditions are all met: * Let $L$ be the length of $X$. $L$ is divisible by both $N$ and $M$. * Concatenating the $1$\-st, $(\frac{L}{N}+1)$\-th, $(2 \times \frac{L}{N}+1)$\-th, $...$, $((N-1)\times\frac{L}{N}+1)$\-th characters of $X$, without changing the order, results in $S$. * Concatenating the $1$\-st, $(\frac{L}{M}+1)$\-th, $(2 \times \frac{L}{M}+1)$\-th, $...$, $((M-1)\times\frac{L}{M}+1)$\-th characters of $X$, without changing the order, results in $T$. Determine if there exists a good string. If it exists, find the length of the shortest such string. ## Constraints * $1 \leq N,M \leq 10^5$ * $S$ and $T$ consist of lowercase English letters. * $|S|=N$ * $|T|=M$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $S$ $T$ [samples]

Samples

Input #1

3 2
acp
ae

Output #1

6

For example, the string `accept` is a good string. There is no good string shorter than this, so the answer is $6$.

Input #2

6 3
abcdef
abc

Output #2

\-1

Input #3

15 9
dnsusrayukuaiia
dujrunuma

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Two Abbreviations",
    "description": {
      "content": "You are given a string $S$ of length $N$ and another string $T$ of length $M$. These strings consist of lowercase English letters. A string $X$ is called a **good string** when the following condition",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc028_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ and another string $T$ of length $M$. These strings consist of lowercase English letters.\nA string $X$ is called a **good string** when the following condition...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments