/*
 * I use 0 to represent prime and 1 to represent not prime,
 * because a byte[] is initialized to all 0.
 *
 * Stores prime/not prime in all 8 bits in each byte.
 */

import java.util.ArrayList;

class Sieve {
	public byte[] arr;
	public int maxNum;
	public boolean smallPrimesGenerated = false;

	private int sqrtNum;
	private int numPrimes = 0;
	private int[] primes = null;

	Sieve(int maxNum, byte[] arr) {
		this.maxNum = maxNum;
		this.sqrtNum = (int)Math.ceil(Math.sqrt(maxNum));
		this.arr = arr;
	}
	Sieve(int maxNum) {
		this(maxNum, new byte[(maxNum / 16) + 1]);
	}

	public int[] getPrimes() {
		if (primes == null) {
			primes = new int[(maxNum / ((int)Math.log(maxNum) - 1)) + 1];

			int i = 0;
			primes[i++] = 2;
			for (int p = 3; p < maxNum; p += 2) {
				if (isPrime(p))
					primes[i++] = p;
			}
		}

		return primes;
	}

	// Find all prime numbers.
	public void generatePrimes(int step, int offset) {
		if (!smallPrimesGenerated)
			generateSmallPrimes();

		for (int i = 2 + offset; i <= sqrtNum; i += (step * 2)) {
			if (isPrime(i)) {
				setNotPrimes(i, maxNum);
			}
		}
	}
	public void generatePrimes() {
		generatePrimes(1, 1);
	}

	// Set all multiples of i as not primes
	private void setBigPrimes(int i) {
		int j = 1;
	}

	// Find the first sqrt(n) prime numbers, and set them
	// as not prime.
	public void generateSmallPrimes() {
		smallPrimesGenerated = true;
		for (int i = 3; i <= sqrtNum; i += 2) {
			if (isPrime(i))
				setNotPrimes(i, sqrtNum);
		}
	}

	// Check whether a number is prime (aka if its bit is 0)
	public boolean isPrime(int i) {
		if (i == 2)
			return true;
		if ((i & 1) == 0)
			return false;

		byte b = arr[byteIndex(i)];
		return (b & (1 << bitIndex(i))) == 0;
	}

	// Set all multiples of i under sqrt(n) as not primes
	private void setNotPrimes(int min, int max) {
		int j = min;
		min *= 2;
		int mul = 3;
		while (min <= max) {
			setNotPrime(min);
			min = j * mul;
			mul += 2;
		}
	}

	// Get the byte a number's bit is in
	private int byteIndex(int i) {
		return i >> 4;
	}

	// Get what bit in the byte a number is in
	private int bitIndex(int i) {
		return (i % 16) >> 1;
	}

	// Set a number to be not prime (aka set its bit to 1)
	private void setNotPrime(int i) {

		// No need to store even numbers
		if (i % 2 == 0)
			return;

		int bi = byteIndex(i);
		arr[bi] = (byte)(arr[bi] | (1 << bitIndex(i)));
	}
}