G. All Tied Up
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

FIFA is organizing a football tournament with a group stage. One group contains $$$n$$$ national teams, numbered from $$$1$$$ to $$$n$$$. Each pair of teams in the group will play exactly once.

A win awards $$$3$$$ points to the winning team and $$$0$$$ to the losing team. A draw awards $$$1$$$ point to each team.

Your friend Pedro claims that this group will be so evenly matched that all $$$n$$$ teams will finish the group stage tied on exactly $$$k$$$ points. You want to find out whether this is possible.

"Stoppage time: until they equalize!"

Given $$$n$$$ and $$$k$$$, determine whether results can be assigned to the $$$\frac{n(n-1)}{2}$$$ matches so that every team finishes with exactly $$$k$$$ points. If so, print any set of results that demonstrates this.

Input

The input consists of a single line containing two integers $$$n$$$ and $$$k$$$ ($$$3 \leq n \leq 500$$$, $$$0 \leq k \leq 3n-3$$$), the number of teams and the desired final score of each team, respectively.

Output

If it is impossible for every team to finish with exactly $$$k$$$ points, print -1 on a single line.

Otherwise, print exactly $$$\frac{n(n-1)}{2}$$$ lines, one per match. Each line must have the form $$$a\ s\ b$$$, where $$$a$$$ and $$$b$$$ ($$$1 \leq a,b \leq n$$$, $$$a \neq b$$$) are teams and $$$s$$$ is one of the symbols $$$ \gt $$$, $$$=$$$, or $$$ \lt $$$.

Each pair of teams must appear on exactly one line. The symbols mean:

  • $$$ \gt $$$: team $$$a$$$ beat team $$$b$$$;
  • $$$ \lt $$$: team $$$a$$$ lost to team $$$b$$$;
  • $$$=$$$: the match ended in a draw.

You may print the matches in any order. If several valid answers exist, print any of them.

Examples
Input
4 6
Output
-1
Input
4 4
Output
1 = 2
3 = 4
2 < 3
2 > 4
1 > 3
4 > 1