input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function should return the list of prime numbers. If the input range is invalid or empty, return an empty list.
  assert sieve_of_eratosthenes(1, 20)==[2, 3, 5, 7, 11, 13, 17, 19]
  assert sieve_of_eratosthenes(10, 30)==[11, 13, 17, 19, 23, 29]
  assert sieve_of_eratosthenes(0, 0)==[]
  assert sieve_of_eratosthenes(100, 101)==[101]
  assert sieve_of_eratosthenes(25, 25)==[]
output: def sieve_of_eratosthenes(start, end):
      if start > end or start < 0 or end < 0:
          return []
      if start == end:
          return []
      if start == 1:
          start = 2
      sieve = [True] * (end + 1)
      sieve[0] = sieve[1] = False
      for i in range(2, int(end**0.5) + 1):
          if sieve[i]:
              for j in range(i*i, end + 1, i):
                  sieve[j] = False
      return [i for i in range(start, end + 1) if sieve[i]]