PASTELE

문제

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 - Rj|, |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!

입력

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).

출력

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