from itertools import chain
import operator
import random

def missing1(a, n, seq):
  if n == 1:
    return a
  x = reduce(operator.xor, xrange(a, a + n))
  x = reduce(operator.xor, seq, x)
  return x


def missing2(a, n, seq):
  if n == 2:
    return (a, a + 1)
  x = reduce(operator.xor, xrange(a, a + n))
  x = reduce(operator.xor, seq, x)

  h_bit = 1 << (x.bit_length() - 1)

  a1, a2 = 0, 0
  for x in xrange(a, a + n):
    if x & h_bit:
      a1 ^= x
    else:
      a2 ^= x

  for x in seq:
    if x & h_bit:
      a1 ^= x
    else:
      a2 ^= x
  if a1 > a2:
    return (a2, a1)
  return (a1, a2)


def main():
  for _ in xrange(1000):
    n = random.randint(1, 50000)
    a = random.randint(0, 2147483647 - n + 1)
    pick = random.randint(a, a + n - 1)
    ary = range(a, pick) + range(pick + 1, a + n)
    random.shuffle(ary)
    assert missing1(a, n, ary) == pick, (a, n, pick)

  for _ in xrange(1000):
    n = random.randint(2, 50000)
    a = random.randint(0, 2147483647 - n + 1)
    pick1 = random.randint(a, a + n - 1)
    pick2 = random.randint(a, a + n - 2)
    if pick2 >= pick1:
      pick2 += 1
    else:
      pick1, pick2 = pick2, pick1
    ary = list(
        chain(xrange(a, pick1),
              xrange(pick1 + 1, pick2),
              xrange(pick2 + 1, a + n)))
    random.shuffle(ary)
    assert missing2(a, n, ary) == (pick1, pick2), ((a, n), (pick1, pick2))

if __name__ == '__main__':
  main()