How to arrange the most economical route from Changsha to Changbai Mountain in Jilin?

The southern slope of Changbai Mountain is in Changbai County, Jilin Province. There are long-distance buses to reach Tonghua, Jilin, or you can take a train to Songjiang River and change to long-distance buses. The western slope of Changbai Mountain is on the Songjiang River. The northern slope of Changbai Mountain is in Chibei District (also called Erdaobai River). I don’t know which slope of Changbai Mountain you want to go to. You can take a flight to Yanji City, and then take a long-distance bus to Erdaobaihe. You can take a train from Changchun to Antu Railway Station and take a long-distance bus to Erdaobaihe. You can take a train from Beijing to Tonghua, and take a long-distance bus or train from Tonghua to Songjiang River. You can also take train K7379 from Shenyang North Railway Station to Baihe Station. Baihe Station is very close to Erdaobaihe. I suggest that you go from Changsha to Beijing, change trains from Beijing to Shenyang North, and then go from Shenyang North to Baihe to visit Changbai Mountain.