Sieve of Eratosthenes: Prime Numbers Generation

This problem requires you to implement the Sieve of Eratosthenes algorithm to generate all prime numbers up to a given value n. The algorithm operates in O(n \( \log \log n \)) time complexity and is one of the most efficient ways to identify primes in a given range.

You will be given several test cases. For each test case, read an integer n and generate a list of all prime numbers less than or equal to n in ascending order. If no prime number exists (for example, when n is less than 2), output an empty line.

Note: All formulas required are presented in LaTeX format.

inputFormat

The input is read from stdin and has the following format:

T
n₁
n₂
...
nT

where T is the number of test cases and each nᵢ is an integer indicating the upper limit for generating prime numbers.

outputFormat

For each test case, output a single line on stdout containing all prime numbers up to n separated by a single space. If there are no prime numbers, print an empty line.

## sample

1
10

2 3 5 7

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