Transformable Teacher

AtCoder

IDabc181_e

Time2000ms

Memory256MB

Difficulty—

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 $\large\frac{N+1}2$ pairs. Your 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. You have $M$ forms that you can transform into. Your height in the $i$\-th form is $W_i$. Find the minimum possible sum of the differences in height over all pairs, achieved by optimally choosing your form and making pairs. ## Constraints * All values in input are integers. * $1 \leq N, M \leq 2 \times 10^5$ * $N$ is an odd number. * $1 \leq H_i \leq 10^9$ * $1 \leq W_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $H_1$ $\dots$ $H_N$ $W_1$ $\dots$ $W_M$ [samples]

Samples

Input #1

5 3
1 2 3 4 7
1 3 8

Output #1

3

The minimum is minimized by choosing the form with the height $8$ and making pairs with heights $(1, 2)$, $(3, 4)$, and $(7, 8)$.

Input #2

7 7
31 60 84 23 16 13 32
96 80 73 76 87 57 29

Output #2

Input #3

15 10
554 525 541 814 661 279 668 360 382 175 833 783 688 793 736
496 732 455 306 189 207 976 73 567 759

Output #3

API Response (JSON)

{
  "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+...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments