Non-divisible Set

AtCoder

IDarc141_d

Time2000ms

Memory256MB

Difficulty—

We say that a set $S$ of positive integers is _good_ when, for any $a,\ b \in S\ (a\neq b)$, $b$ is not a multiple of $a$. You are given a set of $N$ integers between $1$ and $2M$ (inclusive): $S=\lbrace A_1,\ A_2,\ \dots,\ A_N\rbrace$. For each $i=1,\ 2,\ \dots,\ N$, determine whether there exists a good set with $M$ elements that is a subset of $S$ containing $A_i$. ## Constraints * $M \leq N \leq 2M$ * $1 \leq M \leq 3 \times 10^5$ * $1 \leq A_1 < A_2 < \dots < A_N \leq 2M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_{N}$ [samples]

Samples

Input #1

5 3
1 2 3 4 5

Output #1

No
Yes
Yes
Yes
Yes

Trivially, the only good set containing $A_1=1$ is $\lbrace 1\rbrace$, which has just one element, so the answer for $i=1$ is `No`.
There is a good set $\lbrace 2,\ 3,\ 5\rbrace$ containing $A_2=2$, so the answer for $i=2$ is `Yes`.

Input #2

4 4
2 4 6 8

Output #2

No
No
No
No

Input #3

13 10
2 3 4 6 7 9 10 11 13 15 17 19 20

Output #3

No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No

API Response (JSON)

{
  "problem": {
    "name": "Non-divisible Set",
    "description": {
      "content": "We say that a set $S$ of positive integers is _good_ when, for any $a,\\ b \\in S\\ (a\\neq b)$, $b$ is not a multiple of $a$. You are given a set of $N$ integers between $1$ and $2M$ (inclusive): $S=\\lbr",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc141_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We say that a set $S$ of positive integers is _good_ when, for any $a,\\ b \\in S\\ (a\\neq b)$, $b$ is not a multiple of $a$.\nYou are given a set of $N$ integers between $1$ and $2M$ (inclusive): $S=\\lbr...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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