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_NOutput
Print the answer in the following format.
M
p_1 q_1
p_2 q_2
\vdots
p_M q_MThe 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$b<d$.
样例
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
2 1414213562
0 0
1000000000 1000000000
0
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
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