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Ex - Enumerate Pairs

Score : $600$ points

Problem Statement

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:

$N$ $K$

$x_1$ $y_1$

$x_2$ $y_2$

$\vdots$

$x_N$ $y_N$

Output

Print the answer in the following format.

``` $M$ $p_1$ $q_1$ $p_2$ $q_2$ $\vdots$ $p_M$ $q_M$ ```

The first line should contain an integer $M$, representing the number of pairs of integers to be listed.
The subsequent $M$ lines should contain the pairs of integers to be listed $(p_i,q_i)$ in lexicographical order, each in its own line, separated by a space.
Here, a pair of integers $(a,b)$ comes before a pair of integers $(c,d)$ if and only if one of the following conditions is satisfied.

• $a<c$.
• $a=c$ and $b<d$.

---

6 5
2 0
2 2
3 4
0 0
5 5
8 3

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.
$(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(5,6)$

---

2 1414213562
0 0
1000000000 1000000000

0

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

---

10 150
300 300
300 400
300 500
400 300
400 400
400 400
400 500
500 300
500 400
500 500

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 $y_i=y_j$.