{"raw_statement":[{"iden":"problem statement","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`."},{"iden":"constraints","content":"*   $1 \\leq K \\leq N \\leq 300$\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."},{"iden":"input","content":"Input 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$X_N$ $Y_N$"},{"iden":"sample input 1","content":"5 2\n0 0\n1 0\n0 1\n-1 0\n0 -1"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"1 1\n0 0"},{"iden":"sample output 2","content":"Infinity\n\nInfinitely many lines pass the origin.\nThus, `Infinity` should be printed."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}