Kth Excluded

AtCoder

IDabc205_d

Time3000ms

Memory256MB

Difficulty—

You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \dots, A_N)$, and $Q$ queries. In the $i$\-th query $(1 \leq i \leq Q)$, given a positive integer $K_i$, find the $K_i$\-th smallest integer among the positive integers that differ from all of $A_1, A_2, \dots, A_N$. ## Constraints * $1 \leq N, Q \leq 10^5$ * $1 \leq A_1 < A_2 < \dots < A_N \leq 10^{18}$ * $1 \leq K_i \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $A_1$ $A_2$ $\ldots$ $A_N$ $K_1$ $K_2$ $\vdots$ $K_Q$ [samples]

Samples

Input #1

Output #1

2
9
4

The positive integers that differ from all of $A_1, A_2, \dots, A_N$ are $1, 2, 4, 8, 9, 10, 11, \dots$ in ascending order. The second, fifth, and third smallest of them are $2$, $9$, and $4$, respectively.

Input #2

Output #2

6
15

API Response (JSON)

{
  "problem": {
    "name": "Kth Excluded",
    "description": {
      "content": "You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \\dots, A_N)$, and $Q$ queries. In the $i$\\-th query $(1 \\leq i \\leq Q)$, given a positive integer $K_i$, find the $K_i$\\-th smallest ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc205_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \\dots, A_N)$, and $Q$ queries.\nIn the $i$\\-th query $(1 \\leq i \\leq Q)$, given a positive integer $K_i$, find the $K_i$\\-th smallest ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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