Your challenge, with a POD of no earlier then 711 AD and no later then 1500, is to create an Islamic state with the great majority of its population being Muslims that controls all of the Iberian Peninsula that lasts until the modern day. Bonus points if the country is a Westernized liberal democracy. Even more bonus points if you can do it with as few changes in OTL history as possible (so that there is still a U.S in ATL, along with the EU, World Wars 1 and 2, Steve Jobs, etc.)