Puzzle of the week #126

Level: 
4-Rook
Chess Diagram: 

-----k--
-----p--
--K--P--
p---Q---
-q-----p
-P------
P-------
--------

Queen endgames are the hardest ones to predict because of their complexity. If Queens are already on the board, there are multiple check moves to consider. If Queens are about to reappear for both sides as a result of pawn promotions, you can stop too soon in your analysis and come up with the wrong conclusion; this actually happened with a couple of answers I got for puzzle #125, answers which were normally wrong and would have ended that endgame in a draw.
This week's puzzle is another end of the game, but this time between 2 Grand Masters of today. Your tasks - White to move and:
a) Decide if the game ends in a draw or a win for one of the sides;
b) Provide the best line to show your correct decision. Explain your solution.

Total available points for this puzzle is 20. The answers will be published next week together with puzzle #127.

Puzzle #125 solution:
I have received some very interesting solutions, but none complete or deep enough. This was actually a very good test to compare your endgame mastery to both players involved: Jacob is rated over 1600 and John is almost 1900. I did not choose any of the answers, but will simply list the correct response:

Black is in perfect position to take advantage of the more advanced pawns it has on the Queen side. This is the correct and fastest winning idea, allowing for two interesting lines:
Line 1: 34... a4! 35.Kxh4 b4 36.axb4 a3 37.b5 a2 38.bxc6 a1Q 0-1 In this one Black just bullies his way into a new Queen and wins with ease.
Line 2: 34... h3! 35.gxh3 a4 36.Kg4 b4 37.axb4 a3 38.b5 a2 39.bxc6 a1Q 0-1 Here Black plays safe by giving White a passed pawn too far away from promotion and blocked by his own King. This would assure Black of winning the foot race for a new Queen beyond a doubt.
An interesting winning line could have been:
38... Kc2 39.g5 b3 40.g6 b2 41.g7 b1Q 42.g8Q Qh1+ 43.Kg3 Qg1+ 0-1
and I thought about it as I was waiting for John's move to appear online; however White has a nice resource on the fact the Bishop is stronger in open positions. The better line for White would be:
39.Bc5! b3 40.Ba3 b2 41.Bxb2 Kxb2 42.g5 Kc3 43.g6 Nd4 44.Kg5 ... and the Black pieces are too far away from the action. The game would end in a draw. I would have given 10 points for this line anyway, but nobody got near this idea!
After missing lines 1 and 2 John played the endgame extremely well.

Correct solutions:
Owen - 25 points
Karl - 20 points
Frank - 15 points
Jeffrey - 8 points
Alex - 4 points

Comment: 

Queen endgame complexity