{"problem":{"name":"Yakiniku Optimization Problem","description":{"content":"Takahashi wants to grill $N$ pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the $i$\\-th piece of meat are $\\left(x_i, y_i\\right)$, and its _hardness","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc157_f"},"statements":[{"statement_type":"Markdown","content":"Takahashi wants to grill $N$ pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the $i$\\-th piece of meat are $\\left(x_i, y_i\\right)$, and its _hardness_ is $c_i$.\nTakahashi can use one heat source to grill the meat. If he puts the heat source at coordinates $\\left(X, Y\\right)$, where $X$ and $Y$ are real numbers, the $i$\\-th piece of meat will be ready to eat in $c_i \\times \\sqrt{\\left(X - x_i\\right)^2 + \\left(Y-y_i\\right)^2}$ seconds.\nTakahashi wants to eat $K$ pieces of meat. Find the time required to have $K$ or more pieces of meat ready if he put the heat source to minimize this time.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 60$\n*   $1 \\leq K \\leq N$\n*   $-1000 \\leq x_i , y_i \\leq 1000$\n*   $\\left(x_i, y_i\\right) \\neq \\left(x_j, y_j\\right) \\left(i \\neq j \\right)$\n*   $1 \\leq c_i \\leq 100$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$x_1$ $y_1$ $c_1$\n$\\vdots$\n$x_N$ $y_N$ $c_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc157_f","tags":[],"sample_group":[["4 3\n-1 0 3\n0 0 3\n1 0 2\n1 1 40","2.4\n\nIf we put the heat source at $\\left(-0.2, 0\\right)$, the $1$\\-st, $2$\\-nd, and $3$\\-rd pieces of meat will be ready to eat within $2.4$ seconds. This is the optimal place to put the heat source."],["10 5\n-879 981 26\n890 -406 81\n512 859 97\n362 -955 25\n128 553 17\n-885 763 2\n449 310 57\n-656 -204 11\n-270 76 40\n184 170 16","7411.2252"]],"created_at":"2026-03-03 11:01:14"}}