Extended Domino Dots

Question

Introduction

Classes have started! And so does the boredom. I decided to doodle in my notebook and started to draw some dots in (IMO) an aesthetically pleasing way. I came up with these numbers:

based on these conditions:
Given (n, m)
1) There must be n dots
2) All dots must lie on an m by m lattice
3) The position of the dots must minimize the spread* from the top left corner
4) The configuration of the dots must be diagonally symmetric as pictured:

*Spread (in this context) is defined as the sum of the distances from the top left dot position (whether or not there is a dot there). For example, the spread of the example above is 0 + 1 + 2 + 1 + √2 + 2 + 2√2 = 6 + 3√2

The Challenge

Come up with an algorithm using that uses natural numbers n and m (where it will always be that n <= m^2) to generate a configuration of dots that follow all the rules above.

Input can be received via STDIN, command-line argument, or function parameter.

Output the pattern to STDOUT or return a string with newlines. Any two different characters may be used in the output. (e.g.

110
100
000

is the same as

**-
*--
---

Shortest Code in Bytes Wins

Example

STDIN: 6 3
STDOUT:

***
**_
*__

The Challenge has Ended!!!

After seven days I decided to declare the winner, but first some special awards!
Fastest code goes to... orlp with his submission in Pyth !
Slowest code goes to... orlp with his submission in Pyth !
Most straightforward code goes to... orlp with his submission in Pyth !
Most confusing code goes to... orlp with his submission in Pyth !
Longest Code goes to... orlp with his submission in Pyth !

And last but not least

Shortest code goes to......... orlp with his submission in Pyth !

Congratulations!

Answer 1

Pyth, 37 bytes

jc:*d*QQiRQhos.aMNf.Am}_dTT.c^UQ2vzNQ

Slow solution. Generates all possible pairs of [0, m), generate all possible n-combinations of those pairs (without repetition). Filter each combination of pairs such that if P is in the combination, so is reverse(P). This guarantees diagonal symmetry. Sort by the sum of distances to the origin. Decode the pairs of numbers as base-m numbers, giving a list of indices. Create a string of spaces except for those indices, putting quotation marks instead. Finally chop into m pieces and join by newlines. Creates outputs like such:

""""
"""
""
"