Turn a canary's hash range into router rules

A canary puts a new version of your agent on a small slice of traffic. Your router hashes each user to a number and sends the user to the canary when that number falls in the canary's range. The router cannot match a range directly. It only matches blocks, and its memory for them is short, so you want as few blocks as you can get.

Write canary_rules(bits, start, count) that returns the fewest rules that cover the canary's range exactly.

Input and output:

• bits: how many bits the hash has, a whole number from 1 to 48. Hash values are the whole numbers from 0 to 2 ** bits - 1.
• start: the first hash value in the range, a whole number in the hash space.
• count: how many hash values the range holds, a whole number from 1 to 2 ** bits.
• Return a list of rules, each [first, size], sorted by first.

Rules:

• A rule [first, size] covers the hash values from first to first + size - 1. Its size must be a power of 2, and first must be a multiple of size. So [8, 4] is a rule, and [6, 4] is not.
• The range is the count hash values in a row from start. Past the last hash value it carries on from 0.
• The rules must cover every value in the range and no value outside it.
• Only one set of rules is the smallest, so there is one right answer.