# 2**28 < fact(12) < 2**29 < 2**32 < fact(13) < 2**33 < 
#   < 2**52 < fact(18) < 2**53 < 2**56 < fact(19) < 2**57

sub choose {
	my($n, $k) = @_;
	my($v, $l);
	$k < 0 and return 0;
	$v = 1;
	$n - $k < $k and
		$k = $n - $k;
	for $l ($n - $k + 1 .. $n)
		{ $v *= $l; }
	for $l (2 .. $k)
		{ $v /= $l; }
	$v;
}

sub each_variation {
	my($n, $callb) = @_;
	my(@a, $k);
	@a = (0) x $n;
	OUT: while (1) {
		&$callb(@a);
		$k = $n;
		IN: {
			0 <= --$k or last OUT;
			2 == ++$a[$k] and do { $a[$k] = 0; redo IN; };
		}
	}
}

if (1) {
	my(@k, @p, @pp, $r, @r, $n);
	for $n (0 .. 6) {
		#warn "= $n";
		@r = ();
		each_variation($n, sub {
			@p = @_;
			@k = perm_decode(@p);
			$r = sprintf "%1d %1d %2d %2d : %s\n", 
				@k[0 .. 3], join(" ", @p);
			push @r, $r;
		});
		print sort @r;	
	}
}

if (0) {
	my(@k, @p, @pp, $r, @r, $n);
	for $n (0 .. 60) {
		warn "= $n";
		@r = ();
		each_variation($n, sub {
			@p = @_;
			@k = perm_decode(@p);
			@pp = perm_encode(@k);
			$r = sprintf "%1d %1d %2d : %s : %s\n", 
				@k[0 .. 2], join(" ", @p), join(" ", @pp);
			join(",", @p) eq join(",", @pp) or do {
				$r = sprintf "%1d %1d %2d : %s : %s\n", 
					@k[0 .. 2], join(" ", @p), join(" ", @pp);
				die "perm_encode wrong: $r";
			};
		});
		warn "ok";
	};
}

if (0) {
	my($n, $k);
	for $n (0 .. 15) {
		for $k (0 .. $n) {
			printf "% 5d", choose($n, $k);
		}
		print "\n";
	}
}

if (0) {
	# 9 3 27
	my($n, $k, $b, $v, @p, $nn, $kk, $vv);
	$b = choose(($n, $k) = (9, 3));
	for $v (27 .. 28) {
		@p = perm_encode($n, $k, $v);
		($nn, $kk, $vv) = perm_decode(@p);
		printf "%d %d %2d : %d %d %2d : %s\n", 
			$n, $k, $v, $nn, $kk, $vv, join(" ", @p);
	}
	warn join(" ", perm_decode(perm_encode(9, 3, 28)));
}


__END__