--description--

The look and say sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...

The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.

It helps to do this out loud:

1 is 'one one' $→ 11$

11 is 'two ones' $→ 21$

21 is 'one two and one one' $→ 1211$

1211 is 'one one, one two and two ones' $→ 111221$

111221 is 'three ones, two twos and one one' $→ 312211$

...

Define $A(n)$, $B(n)$ and $C(n)$ as the number of ones, twos and threes in the $n$'th element of the sequence respectively. One can verify that $A(40) = 31\,254$, $B(40) = 20\,259$ and $C(40) = 11\,625$.

Find $A(n)$, $B(n)$ and $C(n)$ for $n = {10}^{12}$. Give your answer modulo $2^{30}$ as a string and separate your values for $A$, $B$ and $C$ by a comma. E.g. for $n = 40$ the answer would be 31254,20259,11625.

--hints--

lookAndSaySequence() should return a string.

assert.isString(lookAndSaySequence());

lookAndSaySequence() should return the string 998567458,1046245404,43363922.

assert.strictEqual(lookAndSaySequence(), '998567458,1046245404,43363922');

--seed--

--seed-contents--

function lookAndSaySequence() {

  return true;
}

lookAndSaySequence();

--solutions--

// solution required