## Editorial for Facebook Hacker Cup '15 Round 1 P1 - Homework

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**If we precompute the primacity of each number, then answering test cases just takes a sweep over the precomputed results.

To compute the primacity, one option is to use a modified Sieve of Eratosthenes. In the normal sieve, we iterate upwards and whenever we find a prime number, we cross off all multiples of it from our list of primes. Rather than crossing off a multiple, we can add to a counter that keeps track of its primacity.

For example, is prime, so we add to the primacity of , , , , etc. is the next prime, so we add to the primacity of , , , , etc.

The time complexity is the same as the standard sieve, for the integers to .

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