Using filesortが付くのが納得いかない…。

01_ddl.sql

CREATE TABLE `foo` (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `created_at` datetime NOT NULL,
  PRIMARY KEY (`id`,`created_at`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8
PARTITION BY RANGE COLUMNS(created_at) (
  PARTITION p201505 VALUES LESS THAN ('2015-06-01') COMMENT = '2015-06-01' ENGINE = InnoDB,
  PARTITION p201506 VALUES LESS THAN ('2015-07-01') COMMENT = '2015-07-01' ENGINE = InnoDB,
  PARTITION p201507 VALUES LESS THAN ('2015-08-01') COMMENT = '2015-08-01' ENGINE = InnoDB,
  PARTITION p201508 VALUES LESS THAN ('2015-09-01') ENGINE = InnoDB
);

02_select.sql

SELECT `id`, `created_at` FROM `foo` WHERE `id` IN (1, 2, 3, 4, 5) ORDER BY created_at DESC LIMIT 5;

03_explain.txt

+----+-------------+---------------+---------------------------------+-------+---------------+---------+---------+------+------+------------------------------------------+
| id | select_type | table         | partitions                      | type  | possible_keys | key     | key_len | ref  | rows | Extra                                    |
+----+-------------+---------------+---------------------------------+-------+---------------+---------+---------+------+------+------------------------------------------+
|  1 | SIMPLE      | foo           | p201505,p201506,p201507,p201508 | range | PRIMARY       | PRIMARY | 4       | NULL |   15 | Using where; Using index; Using filesort |
+----+-------------+---------------+---------------------------------+-------+---------------+---------+---------+------+------+------------------------------------------+
1 row in set (0.00 sec)

04_show_index.txt

[root@localhost] test> SHOW INDEX FROM foo;
+---------------+------------+------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| Table         | Non_unique | Key_name               | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment | Index_comment |
+---------------+------------+------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| foo           |          0 | PRIMARY                |            1 | id          | A         |    XXXXXXXX |     NULL | NULL   |      | BTREE      |         |               |
| foo           |          0 | PRIMARY                |            2 | created_at  | A         |    XXXXXXXX |     NULL | NULL   |      | BTREE      |         |               |
+---------------+------------+------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
4 rows in set (0.91 sec)