Rotate and Flip

AtCoder

IDabc189_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ pieces on a two-dimensional plane. The coordinates of Piece $i$ are $(X_i,Y_i)$. There may be multiple pieces at the same coordinates. We will do $M$ operations $\mathrm{op}_1, \ldots, \mathrm{op}_M$, one by one. There are four kinds of operations, described below along with their formats in input. * `1`：Rotate every piece $90$ degrees clockwise about the origin; * `2`：Rotate every piece $90$ degrees counterclockwise about the origin; * `3 p`：Move each piece to the point symmetric to it about the line $x=p$; * `4 p`：Move each piece to the point symmetric to it about the line $y=p$. You are given $Q$ queries. In the $i$\-th query, given two integers $A_i$ and $B_i$, print the coordinates of Piece $B_i$ just after the $A_i$\-th operation. Here, the moment just before the $1$\-st operation is considered to be the moment just after "the $0$\-th operation". ## Constraints * All values in input are integers. * $1 \leq N \leq 2\times 10^5$ * $1 \leq M \leq 2\times 10^5$ * $1 \leq Q \leq 2\times 10^5$ * $-10^9 \leq X_i,Y_i \leq 10^9$ * $\mathrm{op}_i$ is in the format of one of the four kinds of operations. * In an operation with the form `3 p` or `4 p`, $-10^9 \leq p \leq 10^9$. * $0 \leq A_i \leq M$ * $1 \leq B_i \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $Y_1$ $\vdots$ $X_N$ $Y_N$ $M$ $\mathrm{op}_1$ $\vdots$ $\mathrm{op}_M$ $Q$ $A_1$ $B_1$ $\vdots$ $A_Q$ $B_Q$ [samples]

Samples

Input #1

Output #1

1 2
2 -1
4 -1
1 4
1 0

Initially, the only piece - Piece $1$ - is at $(1, 2)$. Each operation moves the piece as follows: $(1,2)\to(2,-1)\to(4,-1)\to(1,4)\to(1,0)$.

Input #2

2
1000000000 0
0 1000000000
4
3 -1000000000
4 -1000000000
3 1000000000
4 1000000000
2
4 1
4 2

Output #2

5000000000 4000000000
4000000000 5000000000

API Response (JSON)

{
  "problem": {
    "name": "Rotate and Flip",
    "description": {
      "content": "There are $N$ pieces on a two-dimensional plane. The coordinates of Piece $i$ are $(X_i,Y_i)$. There may be multiple pieces at the same coordinates. We will do $M$ operations $\\mathrm{op}_1, \\ldots, \\",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc189_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ pieces on a two-dimensional plane. The coordinates of Piece $i$ are $(X_i,Y_i)$. There may be multiple pieces at the same coordinates.\nWe will do $M$ operations $\\mathrm{op}_1, \\ldots, \\...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments