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^\text{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^\text{th}~ and the ~j^\text{th}~ crayon is ~\max(|R_i - R_j|, |G_i - G_j|, |B_i - B_j|)~. 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!

Input Specification

The first line of input contains integers ~N~ and ~K~ ~(2 \leq K \leq N \leq 100\,000)~.

The ~i^\text{th}~ of the following ~N~ lines contains three integers ~R_i~, ~G_i~ and ~B_i~ ~(0 \leq R_i, G_i, B_i \leq 255)~.

Output Specification

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.

Scoring

In test cases worth ~50\%~ of total points, ~0 \leq R_i, G_i, B_i \leq 20~ will hold.

In test cases worth additional ~30\%~ of total points, ~0 \leq R_i, G_i, B_i \leq 50~ will hold.

Sample Input 1

2 2
1 3 2
2 6 4

Sample Output 1

3
1 3 2
2 6 4

Sample Input 2

3 2
3 3 4
1 6 4
1 1 2

Sample Output 2

2
3 3 4
1 1 2

Sample Input 3

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

Sample Output 3

2
6 2 7
4 1 5
6 2 6