import itertools
import math
import random
 
 
def rank(p, elements):
  k = len(p)
 
  if k == 1:
    return len(list(e for e in elements if e < p[0]))
 
  head, tail = p[0], p[1:]
 
  n = len(elements) - 1
  num_preceding = len([e for e in elements if e < head])
 
  preceding = num_preceding * (
      math.factorial(n)
      / math.factorial(n - k + 1)
  )
 
  return int(preceding) + rank(tail, elements - {head})
 
 
def unrank(index, n, k):
    return [0]
 
 
n = 4
k = 2
 
for p in sorted(itertools.chain.from_iterable(map(
    lambda x: list(itertools.permutations(x)),
    itertools.combinations(range(n), k)))):
  print((p, rank(list(p), set(range(n)))))
 
n = 2048
k = 24
p = random.sample(range(n), k)
print((p, rank(p, set(range(n)))))
 
num_tests = 0
max_n = 20
max_k = 5
 
for _ in range(num_tests):
  n = random.randint(5, max_n)
  k = random.randint(2, min(max_k, n))
 
  p = random.sample(range(1, n + 1), k)
  elements = set(range(n))
 
  rank_p = rank(p, elements)
  unranked = unrank(rank_p, 0, 0)
 
  if unranked != p:
    print((p, n, rank_p, unranked, rank(unranked, elements)))
    break

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