#!/usr/bin/perl -W

use Math::BigInt;
use strict;

my $length = int($ARGV[0]);
my $numbit = int($ARGV[1]);

# All first rows should end up in this array
my @results;

# This should contain the processing stack
my @queue;

my $start_value  = (2 ** $numbit) - 1;
my $start_factor = $numbit - 1;
my $start_level  = $length - $numbit + 1;

push @queue, [ $start_level, $start_factor, $start_value ];

for my $item (@queue) {
  my ($level, $factor, $value) = @{$item};
  #print "Found Item $factor, $level, $value\n";
  for my $x (1..$level) {
    push @results, $value * (2 ** ($x-1));
  }
  #push @results, $value;
  my $next_level = $level - 1;
  if($next_level) {
    foreach my $next_factor (1..$factor) {
      #print "Calculating value ($value * 2) - ((2 ** $next_factor) -1 )\n";
      my $next_value = ($value * 2) - ((2 ** $next_factor) -1);
      push @queue, [ $next_level, $next_factor, $next_value ];
    }
  }
}

print "MATH: ".join(",", sort @results)."\n";

# Manual Checking
my $max = 2**$length;
for my $r (@results) {
  print "A: ABOVE MAX $r > $max\n" and next if $r > $max;
  my $bin = sprintf("%0".$length."b", $r);
  my $count = ($bin =~ tr/1//);
  print "B: TOO MANY SET BITS $r $bin($count) > $numbit\n" and next if $count > $numbit;
}