use 5.020;      # includes strictures
use warnings;

my (@F1, @recs);

while (my $line = <DATA>)
{
    chomp $line;
    my @F = split '&', $line;
    @F1 = @F if $. == 1;
    die "NF mismatch" unless @F1 == @F;
    push @recs, \@F;

    for my $i (0 .. $#F)
    {
        next    unless defined $F1[$i];
        $F1[$i] = undef unless $F1[$i] eq $F[$i];
    }        
}

my @keep;
defined $F1[$_] || push @keep, $_ for (0 .. $#F1);

print join("\t", @$_[ @keep ]), "\n" for @recs;

__DATA__
a=1&b=1&c=1&d=2&e=&f=3
a=1&b=2&c=3&d=2&e=&f=4
a=1&b=2&c=5&d=1&e=&f=5