Solution for 'Secret Cow Code'

NaN.

I was going through the guide on this thread, and I was stuck on the problem 'Secret Cow Code' here: USA Computing Olympiad

I was able to write the code using the solution on the USACO website, but I don't understand how this snippet specifically works:

while(2*length <= index) {
			length *= 2;
		}
		if(length == index) {
			return parse(s, length-1);
		}
		return parse(s, index - length - 1);

Thanks!