Extended Euclid Modular Inverse in Python

from bisect import bisect_left

# Extended Euclid Modular Inverse in Python
#
# PURPOSE
# Extended Euclid tracks a Bezout coefficient while computing the gcd. When gcd(a,m)=1, that
# coefficient is the modular inverse.
#
# METHOD
# Maintain consecutive remainders and coefficients. Update both with the Euclidean quotient;
# normalize the resulting coefficient into [0,m).
#
# COMPLEXITY
# O(log m) arithmetic steps and O(1) auxiliary space.
#
# CONTRACT
# 0 <= a < modulus, 2 <= modulus <= 10000. Returns -1 if no inverse exists. This bounded
# integer implementation is not constant time or suitable for cryptographic secrets.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 4.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def modular_inverse(a: int, modulus: int) -> int:
    alg_require(type(a) is int and -2147483648 <= a <= 2147483647)
    alg_require(type(modulus) is int and -2147483648 <= modulus <= 2147483647)
    alg_require(modulus >= 2 and modulus <= 10000 and (a >= 0) and (a < modulus))
    old_r: int = modulus
    r: int = a
    old_t: int = 0
    t: int = 1
    quotient: int = 0
    temp: int = 0
    while r != 0:
        quotient = old_r // r
        temp = old_r - quotient * r
        old_r = r
        r = temp
        temp = old_t - quotient * t
        old_t = t
        t = temp
    if old_r != 1:
        return -1
    return (old_t % modulus + modulus) % modulus

a = 3
modulus = 11
result = modular_inverse(a, modulus)
print(result)