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import base64
import math
import random
 
 
def rank_permutation(seq):
  ref = sorted(seq)
  if ref == seq:
    return 0
  else:
    rank = 0
    f = math.factorial(len(seq)-1)
    for x in ref:
        if x < seq[0]:
          rank += f
        else:
          rank += rank_permutation(seq[1:]) if seq[1:] else 0
          return rank
 
 
def unrank_permutation(n, k):
    if not (0 <= k < math.factorial(n)):
        raise ValueError("Rank k is out of bounds.")
 
    items = list(range(n))
    permutation = []
    temp_k = k
 
    for i in range(n, 0, -1):
        index = temp_k // math.factorial(i - 1)
        temp_k %= math.factorial(i - 1)
        permutation.append(items.pop(index))
 
    return permutation
 
 
def rank(comb):
  return sum([
    math.comb(ci, i + 1)
    for i, ci in enumerate(comb)])
 
 
def unrank(N, k):
  comb = []
  n = N
  for r in range(k, 0, -1):
    ci = r - 1
    while math.comb(ci + 1, r) <= n:
      ci += 1
    comb.append(ci)
    n -= math.comb(ci, r)
  return list(reversed(comb))
 
 
def unget(perm, n):
  k = len(perm)
  zipped = zip(perm, range(k))
  zipped2 = [(*a, b) for a, b in zip(sorted(zipped), range(k))]
  zipped_perm = sorted(zipped2, key=lambda x: x[1])
  mapped_perm = map(lambda x: x[2], zipped_perm)
  return rank(list(sorted(perm))), rank_permutation(list(mapped_perm))
 
 
def get(ci, pi, k):
  comb = unrank(ci, k)
  perm = unrank_permutation(k, pi)
  return list(map(lambda i: comb[i], perm))
 
 
num_tests = 100
 
for _ in range(num_tests):
    n = random.randint(2, 2048)
    k = random.randint(1, min(30, n - 1))
    perm = random.sample(range(n - 1), k)
 
    print(n, k)
    print(perm)
    ci, pi = unget(perm, n)
    print((ci, pi))
    bci, bpi = (
      base64.b64encode(str(ci).encode()),
      base64.b64encode(str(pi).encode()))
    print((bci, bpi))
    result = get(ci, pi, len(perm))
    if perm != result:
      print('HHHEEEEEEYYYYY!!!!')
      print(perm, result)
 
print('Done.')

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Success #stdin #stdout 0.51s 15624KB

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1494 8
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1881 18
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304 12
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468 20
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172 2
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912 23
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1079 10
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1295 15
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1798 5
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918 13
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206 17
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430 27
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1093 12
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972 18
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105 21
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1784 26
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863 19
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1946 24
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1286 4
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863 29
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779 7
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1829 11
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1521 18
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1110 19
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1701 7
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882 7
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40 23
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2027 8
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819 7
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151 25
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247 24
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19 3
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1383 15
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904 18
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694 12
[366, 384, 265, 484, 472, 486, 555, 548, 420, 187, 691, 514]
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1092 2
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1235 5
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566 25
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1752 16
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1967 24
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514 11
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1002 2
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1808 8
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1522 30
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1682 14
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1000 18
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1163 18
[899, 929, 805, 748, 892, 1078, 683, 557, 383, 319, 541, 270, 1016, 743, 677, 908, 695, 932]
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1124 7
[696, 194, 811, 104, 772, 1003, 327]
(198800105678557966, 2355)
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112 8
[33, 61, 50, 102, 34, 55, 21, 108]
(370551823457, 8240)
(b'MzcwNTUxODIzNDU3', b'ODI0MA==')
Done.

https://ideone.com/8WJSdo

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Python 3 (python 3.12)

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