<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def validate_lengths(n_samples, lengths):
 """Validate lengths array against n_samples. Parameters n_samples : integer Total number of samples. lengths : array-like of integers, shape (n_sequences,), optional Lengths of individual sequences in the input. Returns ------- start : array of integers, shape (n_sequences,) Start indices of sequences. end : array of integers, shape (n_sequences,) One-past-the-end indices of sequences. """

    if lengths is None:
        lengths = [n_samples]
    lengths = np.asarray(lengths, dtype=np.int32)
    if lengths.sum() > n_samples:
        msg = "More than {0:d} samples in lengths array {1!s}"
        raise ValueError(msg.format(n_samples, lengths))

    end = np.cumsum(lengths)
    start = end - lengths

    return start, end