Constellation

Vadim is an astronomy enthusiast and a member of an astronomy club. Recently, he learned about constellations, which fascinated him. Inspired, he used a telescope to photograph the night sky and began searching for constellations in the image he captured.

To identify constellations, Vadim created a simple rule: a star (A) belongs to the same constellation as all stars whose images are "not too far" from its image. Let (d) be the distance from the image of star (A) to the nearest image of another star. Vadim will include in the same constellation with (A) all stars whose images are at a distance no greater than (k $\cdot$ d), where (k) is an integer chosen by Vadim beforehand.

Vadim applies this rule as follows: stars (A) and (B) are considered to be in the same constellation if there exists a sequence of stars (A = u_1, u_2, ..., 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 conditions is met:

• The distance between their images does not exceed (k $\cdot$ md(u_i)), where (md(X)) is the distance from the image of star (X) to the nearest image of another star.

• The distance between their images does not exceed (k $\cdot$ md(u_i+1)).

Vadim considers two stars to be in the same constellation if such a sequence exists.

Your task is to write a program that, based on the coordinates of the star images in the photo, groups them into constellations according to Vadim's method.

Input

The first line of the input contains two integers: (n) - the number of stars in the photo ((2 $\le$ n $\le$ 5000)) and (k) ((1 $\le$ k $\le$ 10)). Each of the following (n) lines contains two numbers - (x_i) and (y_i) - the coordinates of the image of the next star ((|x_i|, |y_i| $\le$ 10^5)). The images of all stars are at distinct points.

Output

Output (m) - the number of constellations. In the next (m) lines, provide the descriptions of the constellations. Each description should include 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 (1) to (n) in the order they appear in the input.

Examples