Imagawa Ancestors

I am getting conflicting information from some Japanese websites
about the ancestry of the Imagawa. Some sites say the Imagawa are
descended from Kira (Imagawa) Kuniuji, the son of Kira Nagauji.
Others say that Kuniuji is actually the son of Ashikaga Ariuji, and
was adopted by Nagauji.

Here are three sites I've looked at:

http://www15.u-page.so-net.ne.jp/kc4/tomofumi/page001.html

http://village.infoweb.ne.jp/~isamun/monarchs/people/japan/imagawa.htm
l

http://www2.harimaya.com/sengoku/html/imaga_k.html

Could someone explain the relationship between Nagauji and Kuniuji?

Thanks