Do commercial flights avoid flying over China?

I noticed that flights from Europe to Japan seem to avoid China, is that because of China or for other technical reasons?
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Every time you cross an ATC boundary, you pay a fee. The flight already paid Russia the ATC fees for the long flight over their territory, why would they pay China too, to save just a bit in fuel costs?

PS: That is unless the country is in an bi-lateral agreement with the flight operator country, then they don’t pay any fees (EU countries for example, USA ATC is free, etc.).
https://aviation.stackexchange.com/questions/25047/are-there-fees-for-international-flights-crossing-through-another-countrys-airs

makes sense, thanks…

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