Implement greedy decoding and beam search

You are given access to an auto-regressive language model that can score the next token based on a prefix. Assume: - `next_logprobs(prefix_tokens) -> Map[token, logp]` returns log-probabilities (natural log) for the next token given the current prefix. - `EOS` is a special end-of-sequence token. - You are also given `max_len` and an initial prefix `prompt_tokens`. Implement two decoding methods: 1) **Greedy decoding (greedy sampling)** - Repeatedly select the single token with the highest log-probability at each step. - Stop when you generate `EOS` or when the total length reaches `max_len`. - Return the generated token sequence (including the prompt, or clearly specify whether you return only newly generated tokens). 2) **Beam search (keep top-k paths)** - Given an integer `k` (the number of beams to keep), implement beam search that maintains the **top-k candidate sequences** by total sequence score. - Use **cumulative log-probability** (sum of token log-probs) as the sequence score (no need for length normalization unless you choose to add it and explain). - At each decoding step, expand each current beam by one token using `next_logprobs`, then keep only the top-k resulting sequences overall. - Stop when all beams have generated `EOS` or when reaching `max_len`. - Return the best sequence (and optionally the top-k sequences if requested). Clarify any edge cases you handle (e.g., early-finished beams, ties, empty vocabulary, whether finished beams remain in the beam set without further expansion).