GCD Sequence

AtCoder

IDagc022_b

Time2000ms

Memory256MB

Difficulty—

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers. She thinks that a set $S = {a_{1}, a_{2}, ..., a_{N}}$ of **distinct** positive integers is called **special** if for all $1 \leq i \leq N$, the gcd (greatest common divisor) of $a_{i}$ and the sum of the remaining elements of $S$ is **not** $1$. Nagase wants to find a **special** set of size $N$. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a **special** set of size $N$ such that the gcd of all elements are $1$ and the elements of the set does not exceed $30000$. ## Constraints * $3 \leq N \leq 20000$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

2 5 63

${2, 5, 63}$ is special because $gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7$. Also, $gcd(2, 5, 63) = 1$. Thus, this set satisfies all the criteria.
Note that ${2, 4, 6}$ is not a valid solution because $gcd(2, 4, 6) = 2 > 1$.

Input #2

Output #2

2 5 20 63

${2, 5, 20, 63}$ is special because $gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9$. Also, $gcd(2, 5, 20, 63) = 1$. Thus, this set satisfies all the criteria.

API Response (JSON)

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    "name": "GCD Sequence",
    "description": {
      "content": "Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers. She thinks that a set $S = {a_{1}, a_{2}, ..., a_{N}}$ of **distinct** positive i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc022_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.\nShe thinks that a set $S = {a_{1}, a_{2}, ..., a_{N}}$ of **distinct** positive i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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