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Mirko recently got `N` crayons as a gift. The color of each crayon is a combination of three primary colors: red, green and blue. The color of the `i`th crayon is represented with three integers: `R_i` for the red, `G_i` for the green and `B_i` for the blue component.

The difference between the `i`th and the `j`th crayon is `max(|R_i\ -\ R_j|,\ |G_i\ -\ "Gj"|,\ |"Bi"\ -\ "Bj"|)`. The colorfulness of a subsequence of crayons is equal to the largest difference between any two crayons in the subsequence.

Mirko needs a subsequence with `K` crayons with the smallest colorfulness for his drawing. The subsequence does not have to be consecutive. Find it!

The first line of input contains integers `N` and `K` (`2\ ≤\ K\ ≤\ N\ ≤\ 100\ 000`). The `i`th of the folowing `N` lines contains three integers `R_i`, `G_i`, and `B_i` (`0\ ≤\ R_i,\ G_i,\ B_i\ ≤\ 255`).

The first line of output should contain the smallest colorfulness of a subsequence with `K` crayons. The following `K` lines should contain the `R`, `G` and `B` values of the colors of the crayons in the subsequence, in any order. Any subsequence that yields the smallest colorfulness will be accepted.

2 2
1 3 2 
2 6 4

3 
1 3 2 
2 6 4 

3 2 
3 3 4 
1 6 4 
1 1 2 

2 
3 3 4 
1 1 2 

5 3 
6 6 4 
6 2 7 
3 1 3 
4 1 5 
6 2 6 

2 
6 2 7 
4 1 5 
6 2 6