How did the Kyrgyz defeat the Uighur empire in the ninth century?

In 840 CE, the Kyrgyz successfully overthrew the Uighur empire in Mongolia, bringing an abrupt end to their rule.12

While historical records regarding the specific military tactics or details of this conflict are virtually nonexistent—largely because the Kyrgyz did not engage in campaigns against China and remained outside the mainstream of Inner Asian history—it is known that the Kyrgyz originated from the upper reaches of the Yenisey River in north-central Siberia. Following their victory, the Kyrgyz did not settle in the conquered territory, preferring to remain a forest-dwelling people. The defeated Uighurs subsequently fled and established a new, prosperous kingdom in the Turfan region.123