code: def test_binomial_Mod_slow():
      p, q = 10**5 + 3, 10**9 + 33  # prime modulo
      r, s = 10**7 + 5, 33333333  # composite modulo
  
      n, k, m = symbols("n k m")
      assert (binomial(n, k) % q).subs({n: s, k: p}) == Mod(
          binomial(s, p), q
      )
      assert (binomial(n, k) % m).subs({n: 8, k: 5, m: 13}) == 4
      assert (binomial(9, k) % 7).subs(k, 2) == 1
  
      # Lucas Theorem
      assert Mod(binomial(123456, 43253, evaluate=False), p) == Mod(
          binomial(123456, 43253), p
      )
      assert Mod(binomial(-178911, 237, evaluate=False), p) == Mod(
          -binomial(178911 + 237 - 1, 237), p
      )
      assert Mod(binomial(-178911, 238, evaluate=False), p) == Mod(
          binomial(178911 + 238 - 1, 238), p
      )
  
      # factorial Mod
      assert Mod(binomial(9734, 451, evaluate=False), q) == Mod(
          binomial(9734, 451), q
      )
      assert Mod(binomial(-10733, 4459, evaluate=False), q) == Mod(
          binomial(-10733, 4459), q
      )
      assert Mod(binomial(-15733, 4458, evaluate=False), q) == Mod(
          binomial(-15733, 4458), q
      )
      assert Mod(binomial(23, -38, evaluate=False), q) is S.Zero
      assert Mod(binomial(23, 38, evaluate=False), q) is S.Zero
  
      # binomial factorize
      assert Mod(binomial(753, 119, evaluate=False), r) == Mod(
          binomial(753, 119), r
      )
      assert Mod(binomial(3781, 948, evaluate=False), s) == Mod(
          binomial(3781, 948), s
      )
      assert Mod(binomial(25773, 1793, evaluate=False), s) == Mod(
          binomial(25773, 1793), s
      )
      assert Mod(binomial(-753, 118, evaluate=False), r) == Mod(
          binomial(-753, 118), r
      )
      assert Mod(binomial(-25773, 1793, evaluate=False), s) == Mod(
          binomial(-25773, 1793), s
      )
  
imports: from sympy.concrete.products import Product
  from sympy.core.function import expand_func
  from sympy.core.mod import Mod
  from sympy.core.mul import Mul
  from sympy.core import EulerGamma
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol, symbols
  from sympy.functions.combinatorial.factorials import ff, rf, binomial, factorial, factorial2
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.functions.special.gamma_functions import gamma, polygamma
  from sympy.polys.polytools import Poly
  from sympy.series.order import O
  from sympy.simplify.simplify import simplify
  from sympy.core.expr import unchanged
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.factorials import subfactorial
  from sympy.functions.special.gamma_functions import uppergamma
  from sympy.testing.pytest import XFAIL, raises, slow
label_desc: Use image node_id 14 for calling a global function with example usage: test_binomial_Mod_slow() without return types