text: """M plus N generation."""
  
  from __future__ import annotations
  
  from typing import Callable
  
  import numpy as np
  from scipy import interpolate
  
  RAND_SEED = 12345
  SAMPLE_SIZE = 100000
  
  # ------------------------------------------------------------------------------
  # "M plus N" simulation
  # ------------------------------------------------------------------------------
  
  
  def mplusn_mc(
      m: int,
      n: int,
      specified: bool = False,
      max_delta: float = 5,
      steps: int = 300,
      seed: int = RAND_SEED,
      sample_size: int = SAMPLE_SIZE,
  ) -> Callable:
      """Monte Carlo simulation for M + N method.
  
      Args:
          m: TODO.
          n: TODO.
          specified: TODO.
          max_delta: TODO.
          steps: TODO.
          seed: TODO.
          sample_size: TODO.
  
      Returns:
          TODO.
  
      Raises:
          ValueError: If `m` is smaller than `n`.
      """
      if m < n:
          raise ValueError("Invalid combination of parameters. M >= N expected.")
  
      delta = np.linspace(0, max_delta, steps)
      prop = []
      k = m - n
  
      def _func1(a, b):
          return np.mean(a[-1] < b[0])
  
      def _func2(a, b):
          cond1 = a[-1] < b[0]
          cond2 = a[0] > b[-1]
          return np.mean(cond1 | cond2)
  
      def _func3(a, b):
          cond1 = ((b[k] - b[k - 1]) < (b[0] - a[n - 1])) & (a[-1] < b[0])
          cond2 = ((b[n] - b[n - 1]) < (a[0] - b[m - 1])) & (a[0] > b[-1])
          return np.mean(cond1 | cond2)
  
      # Specified test
      if specified:
          p = _func1
      # Test with M = N
      elif k == 0:
          p = _func2
      # Test with M > N
      else:
          p = _func3
  
      # Seed the random number generator
      np.random.seed(seed=seed)
      for d in delta:
          # Samples from A ~ N(0,1)
          A = np.random.randn(n, sample_size)
  
          # Samples from B ~ N(d,1)
          B = np.random.randn(m, sample_size) + d
  
          # Sort corresponding n-tuples
          A.sort(axis=0)
          B.sort(axis=0)
          pc = p(A, B)
  
          prop.append(pc)
  
      f = interpolate.interp1d(delta, prop)
      return f
  