#!/usr/bin/perl -w
use strict;

# Here are some stubs so you can test my code.

# Replace this with a Fisher Yates shuffle:
sub PermuteList {
    my $av= shift @_;
    print "Not shuffling ( $av->[0] .. $av->[-1] )\n";
}

# Replace these with your own code:
sub GetPopulation { return( 100..(99+$ARGV[0]) ); }
sub ProcessSample { print "( @_ )\n"; }

sub Lcd
{
    my( $x, $y )= @_;
    while( 1 ) {
        if(  $y < $x  ) {
            ( $x, $y )= ( $y, $x );
        }
        if(  $x == 0  ) {
            return $y;
        }
        $y %= $x;
    }
}

sub GenNextSample
{
    my( $size, @list )= @_;
    my $step = @list;
    my( $start, $offset );
    return sub {
        while( 1 ) {
            if(  @list/2 <= $step  ) {
                $step= 1;
                PermuteList( \@list );
                $offset= $start= int rand @list;
            }
            if(  1 == Lcd( $step, 0+@list )  ) {
                my @sample;
                do {
                    return @sample
                        if  $size == @sample;
                    push @sample, $list[$offset];
                    $offset= ( $offset + $step ) % @list;
                } while(  $offset != $start  );
            }
            $step++;
        }
    };
}

my $size= $ARGV[1];
my $iter= GenNextSample( $size, GetPopulation() );
my $samples = 0;
while(  $samples++ < 64000  ) {
    my @sample = $iter->();
    ProcessSample( @sample );
}

##</code><code>##

 > perl lcd.pl 16 3 | more
Not shuffling ( 100 .. 115 )
( 112 113 114 )
( 115 100 101 )
( 102 103 104 )
( 105 106 107 )
( 108 109 110 )
( 112 115 102 )
( 105 108 111 )
( 114 101 104 )
( 107 110 113 )
( 100 103 106 )
( 112 101 106 )
( 111 100 105 )
( 110 115 104 )
( 109 114 103 )
( 108 113 102 )
( 112 103 110 )
( 101 108 115 )
( 106 113 104 )
( 111 102 109 )
( 100 107 114 )
Not shuffling ( 100 .. 115 )
( 102 103 104 )
...