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.

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.

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.

Sample Input 1

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

Sample 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)

Sample Input 2

2 1414213562
0 0
1000000000 1000000000

Sample Output 2

0

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

Sample Input 3

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

Sample 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.

见题面 Input 部分

见题面 Output 部分