IMO, the CJK character in BMP is enough for a input method in daily use.
It contains "CJK Unified Ideographs"(U+4E00 - U+9FFF) and its A
extension(U+3400 - U+4DBF). 

It'll be perfect if we also support the B extension (U+20000 - U+2A6D6),
but rarely used (and even many fonts cannot display these characters). 
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Zihao