{"problem":{"name":"Light It Up","description":{"content":"There are $N$ people numbered $1, 2, \\dots, N$ in the $xy$\\-plane. Person $i$ is at the coordinates $(X_i, Y_i)$.   $K$ of these people, Persons $A_1, A_2, \\dots, A_K$, will receive lights of the same","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc255_b"},"statements":[{"statement_type":"Markdown","content":"There are $N$ people numbered $1, 2, \\dots, N$ in the $xy$\\-plane. Person $i$ is at the coordinates $(X_i, Y_i)$.  \n$K$ of these people, Persons $A_1, A_2, \\dots, A_K$, will receive lights of the same strength.  \nWhen a person at coordinates $(x, y)$ has a light of strength $R$, it lights up the interior of a circle of radius $R$ centered at $(x, y)$ (including the boundary).  \nFind the minimum strength of the lights needed for every person to be lit by at least one light.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\le K < N \\le 1000$\n*   $1 \\le A_1 < A_2 < \\dots < A_K \\le N$\n*   $|X_i|,|Y_i| \\le 10^5$\n*   $(X_i,Y_i) \\neq (X_j,Y_j)$, if $i \\neq j$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\dots$ $A_K$\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":"abc255_b","tags":[],"sample_group":[["4 2\n2 3\n0 0\n0 1\n1 2\n2 0","2.23606797749978969\n\nThis input contains four people. Among them, Persons $2$ and $3$ will have lights.  \nEvery person will be lit by at least one light if $R \\ge \\sqrt{5} \\approx 2.236068$."],["2 1\n2\n-100000 -100000\n100000 100000","282842.712474619009"],["8 3\n2 6 8\n-17683 17993\n93038 47074\n58079 -57520\n-41515 -89802\n-72739 68805\n24324 -73073\n71049 72103\n47863 19268","130379.280458974768"]],"created_at":"2026-03-03 11:01:14"}}