Josephus Survivor in Python

from bisect import bisect_left

# Josephus Survivor in Python
#
# PURPOSE
# The Josephus recurrence finds the last survivor when every kth person in a circle is
# eliminated.
#
# METHOD
# Start with survivor index zero for a one-person circle. Grow the circle one person at a
# time using survivor=(survivor+k) modulo size.
#
# COMPLEXITY
# O(n) time, O(1) space.
#
# CONTRACT
# 1 <= n <= 1000000, 1 <= k <= 1000000. Returns a zero-based survivor index.
# 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: 3.
# 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 josephus(n: int, k: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(type(k) is int and -2147483648 <= k <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(n >= 1 and n <= 1000000 and (k >= 1) and (k <= 1000000))
    survivor: int = 0
    size: int = 2
    while size <= n:
        survivor = (survivor + k) % size
        size += 1
    return survivor

n = 7
k = 3
result = josephus(n, k)
print(result)