a = vector(2^13-1)
u = 1

T = [1]
n = 0
m = 0
emit(t) = {
	if (n++ > #T,
		T = concat(T, vector(#T));
	);
	T[n] = t;
	apply (v -> w = v + 2^exponent(m++); if (w <= #a, a[w] = m), t);
	while (a[u],
		print (u " " a[u]);
		if (u++ > #a,
			quit;
		);
	);
}

{
	emit([0]);
	for (k = 1, oo,
		my (t = T[k]);

		if (#t > 1,
			emit(2*t[2..#t]);
		);
		emit(concat(
			[2*t[1]+0, 2*t[1]+1],
			[2*v+1 | v <- t[2..#t]]
		));
	);
}

quit