{"problem":{"name":"Transformable Teacher","description":{"content":"There are $N$ children in a kindergarten. The height of the $i$\\-th child is $H_i$. Here, $N$ is an odd number. You, the teacher, and these children - $N+1$ people in total - will make $\\large\\frac{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":"abc181_e"},"statements":[{"statement_type":"Markdown","content":"There are $N$ children in a kindergarten. The height of the $i$\\-th child is $H_i$. Here, $N$ is an odd number.\nYou, the teacher, and these children - $N+1$ people in total - will make $\\large\\frac{N+1}2$ pairs.\nYour objective is to minimize the sum of the differences in height over those pairs. That is, you want to minimize $\\displaystyle \\sum_{i=1}^{(N+1)/2}|x_i-y_i|$, where $(x_i, y_i)$ is the pair of heights of people in the $i$\\-th pair.\nYou have $M$ forms that you can transform into. Your height in the $i$\\-th form is $W_i$.\nFind the minimum possible sum of the differences in height over all pairs, achieved by optimally choosing your form and making pairs.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N, M \\leq 2 \\times 10^5$\n*   $N$ is an odd number.\n*   $1 \\leq H_i \\leq 10^9$\n*   $1 \\leq W_i \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$H_1$ $\\dots$ $H_N$\n$W_1$ $\\dots$ $W_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc181_e","tags":[],"sample_group":[["5 3\n1 2 3 4 7\n1 3 8","3\n\nThe minimum is minimized by choosing the form with the height $8$ and making pairs with heights $(1, 2)$, $(3, 4)$, and $(7, 8)$."],["7 7\n31 60 84 23 16 13 32\n96 80 73 76 87 57 29","34"],["15 10\n554 525 541 814 661 279 668 360 382 175 833 783 688 793 736\n496 732 455 306 189 207 976 73 567 759","239"]],"created_at":"2026-03-03 11:01:14"}}