Semi Common Multiple

AtCoder

IDabc150_d

Time2000ms

Memory256MB

Difficulty—

Given are a sequence $A= {a_1,a_2,......a_N}$ of $N$ positive even numbers, and an integer $M$. Let a _semi-common multiple_ of $A$ be a positive integer $X$ that satisfies the following condition for every $k$ $(1 \leq k \leq N)$: * There exists a non-negative integer $p$ such that $X= a_k \times (p+0.5)$. Find the number of semi-common multiples of $A$ among the integers between $1$ and $M$ (inclusive). ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq M \leq 10^9$ * $2 \leq a_i \leq 10^9$ * $a_i$ is an even number. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

2 50
6 10

Output #1

2

*   $15 = 6 \times 2.5$
*   $15 = 10 \times 1.5$
*   $45 = 6 \times 7.5$
*   $45 = 10 \times 4.5$

Thus, $15$ and $45$ are semi-common multiples of $A$. There are no other semi-common multiples of $A$ between $1$ and $50$, so the answer is $2$.

Input #2

3 100
14 22 40

Output #2

0

The answer can be $0$.

Input #3

5 1000000000
6 6 2 6 2

Output #3

166666667

API Response (JSON)

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  "problem": {
    "name": "Semi Common Multiple",
    "description": {
      "content": "Given are a sequence $A= {a_1,a_2,......a_N}$ of $N$ positive even numbers, and an integer $M$. Let a _semi-common multiple_ of $A$ be a positive integer $X$ that satisfies the following condition for",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc150_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are a sequence $A= {a_1,a_2,......a_N}$ of $N$ positive even numbers, and an integer $M$.\nLet a _semi-common multiple_ of $A$ be a positive integer $X$ that satisfies the following condition for...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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