C1: Doubling Powers

Problem Statement

You are given an integer $n$ and two positive integers $a$ and $L$ that are coprime.

For arbitrary integer $k$ satisfying $0 \leq k < n$, calculate $a^{2^k}\ \text{mod}\ L$.

Constraints

• $1 \leq n \leq 10^5$
• $1 \leq a < L \leq 2^{1024}$
• Results must be returned as a Python's list in the form of [$a^{2^0}\ \text{mod}\ L$, $\cdots$, $a^{2^{n-1}}\ \text{mod}\ L$].
• The submitted code must follow the specified format:

def solve(n: int, a: int, L: int) -> list[int]:
    result: list[int] = []
    # Write your code here:
 
    return result