#!perl
use strict;
use warnings;
use Max::Bins;

my $max = $ARGV[0] || 30;
my @can = sort {$a <=> $b} map {int(rand $max) + 1} 1 .. 10;
my @work;

my $next = progressive($max, @can);
while (my @group = $next->()) {
    my ($pick, $left) = avail(\@can, $max, @group);
    next if ! $pick;
    push @work, {left => $left, depth => 1, path => $pick};
}
my ($path, $water_mark) = ('', 1);

while (@work) {
    my $choice = pop @work;
    my @can = @{$choice->{left}};
    my $next = progressive($max, @can);
    while (my @group = $next->()) {
        my ($pick, $left) = avail(\@can, $max, @group);
        next if ! $pick;
        my $depth = $choice->{depth} + 1;
        my $way   = $choice->{path} . ":$pick";
        ($path, $water_mark) = ($way, $depth) if $depth > $water_mark;
        push @work, {left => $left, depth => $depth, path => $way} if @$left + $depth > $water_mark;
    }
}
print $path;