<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def volume_infos(pool=None, volume=None, **kwargs):
    '''
    Provide details on a storage volume. If no volume name is provided, the infos
    all the volumes contained in the pool are provided. If no pool is provided,
    the infos of the volumes of all pools are output.

    :param pool: libvirt storage pool name (default: ``None``)
    :param volume: name of the volume to get infos from (default: ``None``)
    :param connection: libvirt connection URI, overriding defaults
    :param username: username to connect with, overriding defaults
    :param password: password to connect with, overriding defaults

    .. versionadded:: Neon

    CLI Example:

    .. code-block:: bash

        salt "*" virt.volume_infos <pool> <volume>
    '''
    result = {}
    conn = __get_conn(**kwargs)
    try:
        backing_stores = _get_all_volumes_paths(conn)
        domains = _get_domain(conn)
        domains_list = domains if isinstance(domains, list) else [domains]
        disks = {domain.name():
                 {node.get('file') for node
                  in ElementTree.fromstring(domain.XMLDesc(0)).findall('.//disk/source/[@file]')}
                 for domain in domains_list}

        def _volume_extract_infos(vol):
            '''
            Format the volume info dictionary

            :param vol: the libvirt storage volume object.
            '''
            types = ['file', 'block', 'dir', 'network', 'netdir', 'ploop']
            infos = vol.info()

            # If we have a path, check its use.
            used_by = []
            if vol.path():
                as_backing_store = {path for (path, all_paths) in backing_stores.items() if vol.path() in all_paths}
                used_by = [vm_name for (vm_name, vm_disks) in disks.items()
                           if vm_disks & as_backing_store or vol.path() in vm_disks]

            return {
                'type': types[infos[0]] if infos[0] < len(types) else 'unknown',
                'key': vol.key(),
                'path': vol.path(),
                'capacity': infos[1],
                'allocation': infos[2],
                'used_by': used_by,
            }

        pools = [obj for obj in conn.listAllStoragePools() if pool is None or obj.name() == pool]
        vols = {pool_obj.name(): {vol.name(): _volume_extract_infos(vol)
                                  for vol in pool_obj.listAllVolumes()
                                  if (volume is None or vol.name() == volume) and _is_valid_volume(vol)}
                for pool_obj in pools}
        return {pool_name: volumes for (pool_name, volumes) in vols.items() if volumes}
    except libvirt.libvirtError as err:
        log.debug('Silenced libvirt error: %s', str(err))
    finally:
        conn.close()
    return result