import torch


def beam_search(model, start_token, end_token, k, max_len=100):
    """
    Beam search implementation for language model decoding.
    :param model: the model to use for decoding
    :param start_token: the start token
    :param end_token: the end token
    :param k: the number of beams to use
    :param max_len: the maximum length of the sequence to generate
    :return: the list of decoded sequences
    """
    model.eval()
    # Initialize the starting input
    k_sequences = [[[start_token], 0.0]]
    # Iterate until we have k sequences of length max_len
    for _ in range(max_len):
        # Initialize the list of new sequences
        new_sequences = []
        # Iterate over the current sequences
        for sequence, score in k_sequences:
            # Get the last token of the sequence
            last_token = sequence[-1]
            # Get the logits for the next token
            logits, _ = model(sequence)
            # Get the top k logits
            top_k_logits = torch.topk(logits[0, -1, :], k)[0]
            # Iterate over the top k logits
            for logit in top_k_logits:
                # Get the new token
                new_token = torch.multinomial(torch.softmax(logit, dim=0), 1)[0]
                # Get the new score
                new_score = score + logit.item()
                # Add the new sequence to the list of new sequences
                new_sequences.append([sequence + [new_token], new_score])
        # Sort the new sequences by score
        new_sequences.sort(key=lambda x: x[1], reverse=True)
        # Get the best k sequences
        k_sequences = new_sequences[:k]
    # Return the best k sequences
    return k_sequences