Output Combinations

Problem Description

Permutation and combination are common mathematical methods. A combination draws $r$ elements from $n$ elements (order does not matter, and $r \le n$). We can simply understand the $n$ elements as the natural numbers $1,2,\dots,n$, and take any $r$ of them.

Now you are asked to output all combinations.

For example, with $n=5, r=3$, all combinations are:

$123,124,125,134,135,145,234,235,245,345$.

Input Format

One line with two natural numbers $n,r\;(1<n<21,\;0 \le r \le n)$.

Output Format

All combinations, each combination on its own line with its elements in ascending order, and each element occupying three character positions; all combinations are also in lexicographic order.

Note! When outputting, each number needs a field width of $3$. In C++ for example, you can use the following code:

cout << setw(3) << x;

This outputs the number $x$ in a field width of $3$. Note you need the header iomanip.

Sample Input

5 3

Sample Output

  1  2  3
  1  2  4
  1  2  5
  1  3  4
  1  3  5
  1  4  5
  2  3  4
  2  3  5
  2  4  5
  3  4  5