One Time Swap 2

AtCoder

IDabc431_g

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$. For a pair of integers $(l, r) \ (1\leq l\lt r\leq N)$, let $f(l,r)$ be the integer sequence obtained by swapping the $l$\-th element and the $r$\-th element of $A$. Generate a sequence of integer sequences $B=(B_1,B_2,\ldots,B_{\frac{N(N-1)}{2}})$ of length $\frac{N(N-1)}{2}$ by the following procedure: * Prepare an empty sequence $B=()$. * For each pair of integers $(l, r)\ (1\leq l\lt r\leq N)$, add $f(l,r)$ to $B$. * Sort $B$ in lexicographical order of sequences. You are given $Q$ queries; process them in order. The $i$\-th query is as follows: * Given an integer $k$, find one pair of integers $(l, r) \ (1\leq l\lt r\leq N)$ such that $B_k=f(l,r)$ and output it. What is lexicographical order of sequences?A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is **lexicographically smaller** than a sequence $T = (T_1,T_2,\ldots,T_{|T|})$ if and only if one of the following two conditions holds. Here, $|S|$ and $|T|$ represent the lengths of $S$ and $T$, respectively. 1. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. 2. There exists an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold: * $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$ * $S_i$ is smaller than $T_i$ (as a number). ## Constraints * $2\leq N\leq 2\times 10^5$ * $1\leq Q\leq 2\times 10^5$ * $1\leq A_i\leq N$ * $1\leq k\leq \frac{N(N-1)}{2}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $A_1$ $A_2$ $\ldots$ $A_N$ $\mathrm{query}_1$ $\mathrm{query}_2$ $\vdots$ $\mathrm{query}_Q$ Each query is given in the following format: $k$ [samples]

Samples

Input #1

Output #1

2 3
2 4
1 2

$f(1, 2) = (2, 1, 1, 2), f(1, 3) = (1, 2, 1, 2), f(1, 4) = (2, 2, 1, 1), f(2, 3) = (1, 1, 2, 2), f(2, 4) = (1, 2, 1, 2), f(3, 4) = (1, 2, 2, 1)$.
The sequence $B$ obtained by sorting these six sequences in lexicographical order is $B=((1, 1, 2, 2), (1, 2, 1, 2), (1, 2, 1, 2), (1, 2, 2, 1), (2, 1, 1, 2), (2, 2, 1, 1))$.

*   For the $1$\-st query, the only $(l,r)$ such that $B_1=(1,1,2,2)=f(l,r)$ is $(l,r)=(2,3)$.
*   For the $2$\-nd query, $(l,r)$ such that $B_3=(1,2,1,2)=f(l,r)$ are $(l,r)=(1,3),(2,4)$. In this case, either one will be considered correct.
*   For the $3$\-rd query, the only $(l,r)$ such that $B_5=(2,1,1,2)=f(l,r)$ is $(l,r)=(1,2)$.

Input #2

10 10
1 1 2 7 6 3 5 7 3 3
21
36
9
17
13
24
7
45
33
1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "One Time Swap 2",
    "description": {
      "content": "You are given an integer sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$. For a pair of integers $(l, r) \\ (1\\leq l\\lt r\\leq N)$, let $f(l,r)$ be the integer sequence obtained by swapping the $l$\\-th ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc431_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$.\nFor a pair of integers $(l, r) \\ (1\\leq l\\lt r\\leq N)$, let $f(l,r)$ be the integer sequence obtained by swapping the $l$\\-th ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments