Score : 1000 points

Problem Statement

Select any integer N between 1000 and 2000 (inclusive), and any integer K not less than 1, then solve the problem below.

Problem

We have N sheets of paper. Write K integers on each of them to satisfy the following conditions:

  • Each integer written must be between 1 and N (inclusive).
  • The K integers written on the same sheet must be all different.
  • Each of the integers between 1 and N must be written on exactly K sheets.
  • For any two sheet, there is exactly one integer that appears on both.

Input

There is no input in this problem.

Output

In the first line, print N and K separated by a space.

In the subsequent N lines, print your solution. The i-th of these lines must contain the K integers written on the i-th sheet, with spaces in between.

Sample Output

3 2
1 2
2 3
3 1

This is an example of a solution for N = 3 and K = 2.

Note that this output will be judged as incorrect, since the constraint on N is not satisfied.