You fail to understand what
@gambit said
The situation in North Korea now can be put entirely to the Chinese, when you got a dog, you need to reign it in, otherwise it don't just bite people who intrude your home, but some time you will get bite too. US reign in Japan and South Korea, but China let North Korea run amok, now if NK come back and bite China in the arse, it will be entirely Chinese own fault. Or you still think you can control North Korea once they have gone full nuclear, then be my guest.
On the other hand, a military solution does not mean South Korea, Japan or US needed to invade North Korea, there are several proposal to be make, one of these are nuclearized Japan and South Korea, which I don't think China will envy this position, the other one is for US to deploy more advance radar around DPRK, which will directly and indirectly spy on China and Russia too, and in the end, this will be on the Chinese, and we already see how President Moon change his mind about THAAD form against it to wanting 4 more of those. For China, this have no one else to blame but the Chinese themselves.
And finally, if Fat Kim really nuke US, it won't just be a few millions American that got kills, there would be millions Chinese if not all will be killed along with the whole of North Korea, some US Cities. US ICBM are 650 ktn + to megatons damage power, a nuke on North Korean/China border where the C&C and missile Silo were will have fall out effectively blown over to the Chinese side of the border (Tianjin is only 160 mile from North Korean Border, Beijing is only 500 mile from the border, how many people live in these two cities and how many you think will be killed by the Fall Out blown off from the border?), which mean when US nuke North Korea, they will nuke China as well, either Chinese government take it and lose a few millions Chinese along with the American, or you nuke the US and the world ends too. I don't know why anyone don't see it, but a nuke attack on American soil by ANYONE will almost certainly be the end of world scenario, if you think the US will lose a few millions people and just sit there and got nuke by the North Korean, well, be my guest too.