Constellation#635
Vadim is passionate about astronomy and has joined an astronomy club. Recently, he learned about constellations, which greatly interested him. One evening, after returning home, he photographed the night sky with a telescope and started searching for constellations in the resulting image.
To identify constellations, Vadim devised a simple rule: a star is in the same constellation as all stars whose images are "not too far" from its own image. Let denote the distance from the image of star to the nearest image of another star. Vadim includes in the same constellation as all stars whose images are at a distance of no more than k \cdot d, where is an integer Vadim chooses beforehand.
He applies this rule as follows. Stars and are considered to be in the same constellation if there exists a sequence of stars A = u_1, u_2, \ldots, u_l = B such that for any two consecutive stars u_i and u_{i+1} in this sequence, at least one of the following two conditions holds:
The distance between their images does not exceed k \cdot \text{md}(u_i), where denotes the distance from the image of star to the nearest image of another star;
The distance between their images does not exceed k \cdot \text{md}(u_{i+1}).
If such a sequence exists, Vadim considers the two stars to be in the same constellation.
Your task is to write a program that, using the information about the coordinates of the star images in the photo, groups the stars into constellations according to Vadim's method.
The first line of the input contains two integers: — the number of stars in the photo (2 \leq n \leq 5000) and (1 \leq k \leq 10). Each of the next lines contains two numbers — x_i and y_i — the coordinates of the -th star (|x_i|, |y_i| \leq 10^5). The images of all stars are located at distinct points.
On the first line, output the number — the number of constellations. In the following lines, output the descriptions of the constellations. Each description should contain the number n_i — the number of stars in the current constellation, followed by n_i numbers — the indices of these stars. The stars are numbered from to in the order they appear in the input.
Example 1