{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   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*   $1 \\leq c_i \\leq 100$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$x_1$ $y_1$ $c_1$\n$\\vdots$\n$x_N$ $y_N$ $c_N$"},{"iden":"sample input 1","content":"4 3\n-1 0 3\n0 0 3\n1 0 2\n1 1 40"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"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"},{"iden":"sample output 2","content":"7411.2252"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}