def choose_search_strategy(n, q):
    cost_linear = q * n
    cost_binary = n * (n.bit_length()) + q * (n.bit_length())
    cost_hash = n + q
    if cost_linear <= cost_binary and cost_linear <= cost_hash:
        return "linear"
    if cost_binary <= cost_hash:
        return "binary_search_with_sort"
    return "hash_table"


if __name__ == "__main__":
    print(choose_search_strategy(10**3, 1))
    print(choose_search_strategy(10**5, 100))
    print(choose_search_strategy(10**6, 10**6))