Axis-Parallel Rectangle

AtCoder

IDabc075_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ points in a two-dimensional plane. The coordinates of the $i$\-th point $(1 \leq i \leq N)$ are $(x_i,y_i)$. Let us consider a rectangle whose sides are parallel to the coordinate axes that contains $K$ or more of the $N$ points in its interior. Here, points on the sides of the rectangle are considered to be in the interior. Find the minimum possible area of such a rectangle. ## Constraints * $2 \leq K \leq N \leq 50$ * $-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)$ * $x_i≠x_j (1 \leq i<j \leq N)$ * $y_i≠y_j (1 \leq i<j \leq N)$ * All input values are integers. (Added at 21:50 JST) ## Input Input is given from Standard Input in the following format: $N$ $K$ $x_1$ $y_1$ $:$ $x_{N}$ $y_{N}$ [samples]

Samples

Input #1

Output #1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: $(1,1)$, $(8,1)$, $(1,4)$ and $(8,4)$.  
Its area is $(8-1) × (4-1) = 21$.

Input #2

Output #2

Input #3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Output #3

3999999996000000001

Watch out for integer overflows.

API Response (JSON)

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  "problem": {
    "name": "Axis-Parallel Rectangle",
    "description": {
      "content": "We have $N$ points in a two-dimensional plane.   The coordinates of the $i$\\-th point $(1 \\leq i \\leq N)$ are $(x_i,y_i)$.   Let us consider a rectangle whose sides are parallel to the coordinate axes",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "sync_url": null,
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ points in a two-dimensional plane.  \nThe coordinates of the $i$\\-th point $(1 \\leq i \\leq N)$ are $(x_i,y_i)$.  \nLet us consider a rectangle whose sides are parallel to the coordinate axes...",
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