Meanwhile, in 1274, the former Dali Kingdom was officially reorganized as the Province of Yunnan, with Sayyid Ajjal Shams al-Din Omar as governor. In May 1275, the governor sent a report to the emperor stating that the embassy had not returned; that the Burmese evidently had no intention of submitting; and that war was the only way forward. But the emperor rejected an outright invasion. Just coming off a disastrous Japanese campaign, the emperor was unwilling to commit the central government troops to what he considered a low priority affair. He was now focused on delivering the final blow against the Song; the emperor ordered the Yunnan provincial army to secure the borderlands in order to block the escape path of the Song refugees. He also sanctioned a limited border war if Pagan contested the takeover. As planned, the Yunnan army proceeded to consolidate the borderlands in 1275-76. Elsewhere, the main Mongol armies had captured most of the Song territory by 1276. By 1277, at least one Burmese vassal state named "Gold Teeth"  had submitted to the Mongols. Like in 1272, the Burmese government responded by sending an army to reclaim the rebellious state; but unlike in 1272, the Mongols had posted a sizable garrison there. Though it was ultimately under Mongol command, many of the officers and most of the soldiers of the garrison were Turkic-speaking peoples or people from the further west: Turks from Samarkand, Bukhara, Merv and Nishapur, but also captive soldiers from the Persian Khwarazmid empire, the Kipchaks, and even Bulgars from the lower Volga.

Based on the above article, answer a question. How many years did it take after the capture of the Song territory for "Gold Teeth" to submit to the Mongols?
1