Alice, Bob, and Cameron want to get shared key by Diffie-Hellman method. Their public keys respectively are g^a mod p, g^b mod p, g^c mod p. Will Alice and Bob be able to get shared key without Cameron's private key? The flag is the first 20 digits of the shared key in decimal form.

p: 8986158661930085086019708402870402191114171745913160469454315876556947370642799226714405016920875594030192024506376929926694545081888689821796050434591251;
g: 6;
a: 230;
b: 250;
g^c: 5361617800833598741530924081762225477418277010142022622731688158297759621329407070985497917078988781448889947074350694220209769840915705739528359582454617;