Ex - Enumerate Pairs

AtCoder

IDabc234_h

Time4000ms

Memory256MB

Difficulty—

Given are $N$ pairs of integers $(x_i,y_i)$, numbered $1$ to $N$, and an integer $K$. List all pairs of integers $(p,q)$ that satisfy the conditions below, in the format specified in Output. * $1 \le p < q \le N$ * $\sqrt{(x_p-x_q)^2+(y_p-y_q)^2} \le K$ Here, it is guaranteed that there are at most $4 \times 10^5$ such pairs of integers. ## Constraints * All values in input are integers. * $1 \le N \le 2 \times 10^5$ * $1 \le K \le 1.5 \times 10^9$ * $0 \le x_i,y_i \le 10^9$ * There are at most $4 \times 10^5$ pairs of integers that should be listed. ## Input Input is given from Standard Input in the following format: $N$ $K$ $x_1$ $y_1$ $x_2$ $y_2$ $\vdots$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

9
1 2
1 3
1 4
2 3
2 4
2 5
3 4
3 5
5 6

There are $9$ pairs of integers that satisfy the conditions, which should be printed in the specified format.  
$(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(5,6)$

Input #2

2 1414213562
0 0
1000000000 1000000000

Output #2

0

There may be zero pairs of integers that satisfy the conditions.

Input #3

Output #3

29
1 2
1 4
1 5
1 6
2 3
2 4
2 5
2 6
2 7
3 5
3 6
3 7
4 5
4 6
4 8
4 9
5 6
5 7
5 8
5 9
5 10
6 7
6 8
6 9
6 10
7 9
7 10
8 9
9 10

There may be pairs of integers $(i,j)$ ($i < j$) such that $x_i=x_j$ and $y_i=y_j$.

API Response (JSON)

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  "problem": {
    "name": "Ex - Enumerate Pairs",
    "description": {
      "content": "Given are $N$ pairs of integers $(x_i,y_i)$, numbered $1$ to $N$, and an integer $K$.   List all pairs of integers $(p,q)$ that satisfy the conditions below, in the format specified in Output. *   $1",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc234_h"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are $N$ pairs of integers $(x_i,y_i)$, numbered $1$ to $N$, and an integer $K$.  \nList all pairs of integers $(p,q)$ that satisfy the conditions below, in the format specified in Output.\n\n*   $1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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