Complex sentence: The Idiquts (title of the Karakhoja rulers) ruled independently until 1209, when they submitted to the Mongols under Genghis Khan and, as vassal rulers, existed until 1335.
Split into simpler sentences: The Idiquts (title of the Karakhoja rulers) ruled independently until they become vassal state of the Kara-Khitans. In 1209, they submitted to the Mongols under Genghis Khan and, as vassal rulers, existed until 1335.