 Complete the following phrase:  The Amami Islands were a focal point for dispute between the southward-expanding Satsuma Domain and the northward-expanding Ryukyu Kingdom. In 1453, a group of Koreans were shipwrecked on Gaja Island, where they found the island half under the control of Satsuma and half under the control of Ryukyu. Gaja Island is only 80 miles from Satsumas capital at Kagoshima City. The Koreans noted that the Ryukyuans used guns as advanced as in Korea. Other records of activity in the Amami Islands show Shō Tokus conquest of Kikai Island in 1466, a failed Satsuma invasion of Amami Ōshima in 1493, and two rebellions on Amami Ōshima during the 16th century. The islands were finally conquered by Satsuma during the 1609 