K-colinear Line

AtCoder

IDabc248_e

Time2000ms

Memory256MB

Difficulty—

You are given $N$ points in the coordinate plane. For each $1\leq i\leq N$, the $i$\-th point is at the coordinates $(X_i, Y_i)$. Find the number of lines in the plane that pass $K$ or more of the $N$ points. If there are infinitely many such lines, print `Infinity`. ## Constraints * $1 \leq K \leq N \leq 300$ * $\lvert X_i \rvert, \lvert Y_i \rvert \leq 10^9$ * $X_i\neq X_j$ or $Y_i\neq Y_j$, if $i\neq j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$ [samples]

Samples

Input #1

Output #1

6

The six lines $x=0$, $y=0$, $y=x\pm 1$, and $y=-x\pm 1$ satisfy the requirement.  
For example, $x=0$ passes the first, third, and fifth points.
Thus, $6$ should be printed.

Input #2

1 1
0 0

Output #2

Infinity

Infinitely many lines pass the origin.
Thus, `Infinity` should be printed.

API Response (JSON)

{
  "problem": {
    "name": "K-colinear Line",
    "description": {
      "content": "You are given $N$ points in the coordinate plane. For each $1\\leq i\\leq N$, the $i$\\-th point is at the coordinates $(X_i, Y_i)$. Find the number of lines in the plane that pass $K$ or more of the $N$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc248_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ points in the coordinate plane. For each $1\\leq i\\leq N$, the $i$\\-th point is at the coordinates $(X_i, Y_i)$.\nFind the number of lines in the plane that pass $K$ or more of the $N$...",
      "is_translate": false,
      "language": "English"
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}

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