Why mysql fulltext search scan entire table when using "OR"?

Question

My table A is

CREATE TABLE `a` (
  `id` int unsigned NOT NULL AUTO_INCREMENT,
  `content` varchar(255) DEFAULT NULL,
  PRIMARY KEY (`id`),
  FULLTEXT KEY `f_c` (`content`)
) ENGINE=InnoDB AUTO_INCREMENT=6 DEFAULT CHARSET=utf8;

My table B is

CREATE TABLE `b` (
  `id` int unsigned NOT NULL AUTO_INCREMENT,
  `content` varchar(255) DEFAULT NULL,
  `a_id` int DEFAULT NULL,
  PRIMARY KEY (`id`),
  KEY `i_a` (`a_id`),
  FULLTEXT KEY `f_t` (`content`)
) ENGINE=InnoDB AUTO_INCREMENT=4 DEFAULT CHARSET=utf8;

My query is

EXPLAIN 
  SELECT * FROM a 
  LEFT JOIN b ON a.id = b.a_id 
  WHERE MATCH(a.content) AGAINST ("foo") 
          OR MATCH(b.content) AGAINST ("foo");

And the result is mysql scan all rows in table A. Why is it? How to solve it?