Crayons

Changyoung received N crayons as a birthday present. Each crayon's color is represented by three components: red, green, and blue.

The distance between crayon i and crayon j is max(|Ri - Rj|, |Gi - Gj|, |Bi - Bj|). The saturation of a chosen set of crayons is the largest distance among all pairs of crayons in that set.

Choose K of the crayons so that the saturation is as small as possible. Print the minimum possible saturation and one set of K crayons that achieves it.

The first line contains N and K. (2 <= K <= N <= 100,000)

Each of the next N lines contains the color components Ri, Gi, and Bi of one crayon. (0 <= Ri, Gi, Bi <= 255)

On the first line, print the smallest possible saturation after choosing K crayons. On each of the next K lines, print the R, G, and B components of one chosen crayon.

If more than one optimal choice exists, you may print any one of them.