Implement Beam Search With Length Normalization

In a sequence generation model, you are given: - a start token `<bos>` - an end token `<eos>` - a maximum output length `max_len` - a beam size `k` - a function `next_log_probs(prefix)` that returns the log-probability of each possible next token given the current prefix Write a decoder that: 1. Performs greedy decoding when `k = 1`. 2. Performs beam search when `k > 1`, keeping the top `k` candidate hypotheses at each decoding step. 3. Uses cumulative log-probability to score sequences. 4. Returns the best completed sequence, or the best partial sequence if no candidate reaches `<eos>` before `max_len`. Then explain why using raw cumulative log-probability tends to penalize longer sequences, and describe how to reduce this bias using a method such as average log-probability or length normalization.