{"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},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc248_e"},"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 $N$ points.  \nIf there are infinitely many such lines, print `Infinity`.\n\n## Constraints\n\n*   $1 \\leq K \\leq N \\leq 300$\n*   $\\lvert X_i \\rvert, \\lvert Y_i \\rvert \\leq 10^9$\n*   $X_i\\neq X_j$ or $Y_i\\neq Y_j$, if $i\\neq j$.\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$X_1$ $Y_1$\n$X_2$ $Y_2$\n$\\vdots$\n$X_N$ $Y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc248_e","tags":[],"sample_group":[["5 2\n0 0\n1 0\n0 1\n-1 0\n0 -1","6\n\nThe six lines $x=0$, $y=0$, $y=x\\pm 1$, and $y=-x\\pm 1$ satisfy the requirement.  \nFor example, $x=0$ passes the first, third, and fifth points.\nThus, $6$ should be printed."],["1 1\n0 0","Infinity\n\nInfinitely many lines pass the origin.\nThus, `Infinity` should be printed."]],"created_at":"2026-03-03 11:01:13"}}