#! perl -slw
use strict;

sub interleave {
    my( $a, $b ) = qw[ a b ];
    my( $as, $bs ) = @_;
#    ( $a, $as, $b, $bs ) = ( $b, $bs, $a, $as ) if $as < $bs;
    return $a x $as . $b x $bs unless $as and $bs;

    ++$bs;
    my $aPerB = int( $as / $bs );
    my $aRem = $as - $bs * $aPerB;
    my @as = ( $a x $aPerB ) x $bs;
    my $n = 0;
    $as[ $n ] .= $a, $as[ - ++$n ] .= $a, $aRem -= 2 while $aRem > 1;
    $as[ @as / 2 ] .= $a if $aRem > 0;
    return join $b, @as;
}

our $N ||= 10;
our $S ||= 0;
our $M ||= 10;
srand $S if $S;

for ( 13 .. 19 ) {
    my( $na, $nb ) = ( $_, 4 );
    my $s = interleave( $na, $nb );
    my( $as, $bs ) = ( $s =~ tr[a][], $s =~ tr[b][] );
    printf "%2da %2db: %s\n", $na, $nb, $s;
    die "$na != $as or $nb != $bs\n" unless $na == $as and $nb == $bs;
}

print "\n-----------\n";

for ( 1 .. $N ) {
    my( $na, $nb ) = map{ int rand $M } 1 .. 2;
    my $s = interleave( $na, $nb );
    my( $as, $bs ) = ( $s =~ tr[a][], $s =~ tr[b][] );
    printf "%2da %2db: %s\n", $na, $nb, $s;
    die "$na != $as or $nb != $bs\n" unless $na == $as and $nb == $bs;
}


__END__
C:\test>624887 -S=2 -N=20
13a  4b: aaabaabaaabaabaaa
14a  4b: aaabaaabaabaaabaaa
15a  4b: aaabaaabaaabaaabaaa
16a  4b: aaabaaabaaaabaaabaaa
17a  4b: aaaabaaabaaabaaabaaaa
18a  4b: aaaabaaabaaaabaaabaaaa
19a  4b: aaaabaaaabaaabaaaabaaaa

-----------

 0a  8b: bbbbbbbb
 7a  5b: abababaababa
 8a  5b: aabababababaa
 4a  8b: ababbbbbbaba
 3a  5b: abbbabba
 1a  8b: bbbbabbbb
 3a  0b: aaa
 9a  5b: aabababaababaa
 9a  9b: ababababbababababa
 2a  8b: abbbbbbbba
 3a  9b: abbbbbabbbba
 5a  2b: aababaa
 4a  7b: ababbbbbaba
 1a  0b: a
 9a  2b: aaabaaabaaa
 2a  3b: abbba
 8a  1b: aaaabaaaa
 5a  5b: ababbababa
 8a  2b: aaabaabaaa
 6a  5b: abababababa