title: Multiply Large Integers Under Large Modulo
signature: def multiply_large_integers_under_large_modulo(a, b, mod_arg2):
source_py: def multiply_large_integers_under_large_modulo(a, b, mod):
      res = 0
      a = (a % mod)
      while b:
          if (b & 1):
              res = ((res + a) % mod)
          a = ((2 * a) % mod)
          b >>= 1
      return res
source_cpp: long long multiply_large_integers_under_large_modulo(long long a, long long b, long long mod) {
    long long res = 0;
    a %= mod;
    while ( b ) {
      if ( b & 1 ) res = ( res + a ) % mod;
      a = ( 2 * a ) % mod;
      b >>= 1;
    }
    return res;
  }
question_info.test_code: import array
  import bisect
  import collections
  import datetime
  import functools
  import heapq
  import itertools
  import math
  import queue
  import re
  import string
  import sys
  from typing import Any, Dict, List, Optional, Set
  
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  def validate_solution(actual, expected):
      return actual == expected
  
  def driver(a, b, mod_arg2, expected):
      try:
          if validate_solution(PLACEHOLDER_FN_NAME(
              a, b, mod_arg2),
              expected
          ):
              return "PASSED"
          return "FAILED"
      except Exception as exception_obj:
          return type(exception_obj).__name__
      
  if __name__ == "__main__":
      result = driver(60, 24, 58, 48)
      print(f"TEST-0...{result}")
  
      result = driver(46, 43, 29, 6)
      print(f"TEST-1...{result}")
  
      result = driver(4, 50, 71, 58)
      print(f"TEST-2...{result}")
  
      result = driver(67, 1, 66, 1)
      print(f"TEST-3...{result}")
  
      result = driver(93, 35, 73, 43)
      print(f"TEST-4...{result}")
  
      result = driver(89, 97, 8, 1)
      print(f"TEST-5...{result}")
  
      result = driver(8, 78, 55, 19)
      print(f"TEST-6...{result}")
  
      result = driver(53, 73, 22, 19)
      print(f"TEST-7...{result}")
  
      result = driver(96, 92, 83, 34)
      print(f"TEST-8...{result}")
  
      result = driver(38, 64, 83, 25)
      print(f"TEST-9...{result}")
  
      sys.exit(0)
question_info.test_case_ids: ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
question_info.entry_fn_name: multiply_large_integers_under_large_modulo
question_info.test_list: [{"idx": 0, "outputs": 48, "inputs": {"a": 60, "b": 24, "mod_arg2": 58}}, {"idx": 1, "outputs": 6, "inputs": {"a": 46, "b": 43, "mod_arg2": 29}}, {"idx": 2, "outputs": 58, "inputs": {"a": 4, "b": 50, "mod_arg2": 71}}, {"idx": 3, "outputs": 1, "inputs": {"a": 67, "b": 1, "mod_arg2": 66}}, {"idx": 4, "outputs": 43, "inputs": {"a": 93, "b": 35, "mod_arg2": 73}}, {"idx": 5, "outputs": 1, "inputs": {"a": 89, "b": 97, "mod_arg2": 8}}, {"idx": 6, "outputs": 19, "inputs": {"a": 8, "b": 78, "mod_arg2": 55}}, {"idx": 7, "outputs": 19, "inputs": {"a": 53, "b": 73, "mod_arg2": 22}}, {"idx": 8, "outputs": 34, "inputs": {"a": 96, "b": 92, "mod_arg2": 83}}, {"idx": 9, "outputs": 25, "inputs": {"a": 38, "b": 64, "mod_arg2": 83}}]
question_info.entry_cls_name: Solution