KK as overpair, tough river decision

[Jeans]

Poker Room skin
Pot Limit Holdem Ring game
Blinds: $2/$4
2 players
Converter

Stack sizes:
Hero: $407
BB: $414.60

Pre-flop: (2 players) Hero is SB with K[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img]
<font color="#cc0000">Hero raises to $12</font>, BB calls.

Flop: 2[img]/images/graemlins/spade.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 9[img]/images/graemlins/spade.gif[/img] ($24, 2 players)
BB checks, <font color="#cc0000">Hero bets $20</font>, BB calls.

Turn: 7[img]/images/graemlins/heart.gif[/img] ($64, 2 players)
BB checks, <font color="#cc0000">Hero bets $50</font>, BB calls.

River: 4[img]/images/graemlins/club.gif[/img] ($164, 2 players)
<font color="#cc0000">BB bets $200</font>, Hero ?

The table got down to HU. Villain is a 31/14/1 donk, and we don't have very much history, this is a really tough spot imo, I have sometimes seen these types of villains make sick bluffs with missed draws, or perhaps 97 which he thinks is the nuts, dunno if this guy is capable of it
please post your thought I will check this in the morning, thankyou