code: def test_josephus():
      assert Permutation.josephus(4, 6, 1) == Permutation(
          [3, 1, 0, 2, 5, 4]
      )
      assert Permutation.josephus(1, 5, 1).is_Identity
  
imports: from itertools import permutations
  from copy import copy
  from sympy.core.expr import unchanged
  from sympy.core.numbers import Integer
  from sympy.core.relational import Eq
  from sympy.core.symbol import Symbol
  from sympy.core.singleton import S
  from sympy.combinatorics.permutations import Permutation, _af_parity, _af_rmul, _af_rmuln, AppliedPermutation, Cycle
  from sympy.printing import sstr, srepr, pretty, latex
  from sympy.testing.pytest import raises, warns_deprecated_sympy
label_desc: Use image node_id 3 for calling a global function with example usage: test_josephus() without return types