I know they got as far as screwing with Poland and Hungary, but how much further could they go? Could the reach to the Rhine, or even the Atlantic? Could they burn through the Germanies and France? Would Italy and Iberia be in danger?
Were the Byzantines in danger? The Scandinavians, even the British countries? (In a hyperbolic sense I'm not worried for the last ones so much, seeing as how the universe hates invasions of the British isles and would likely just give the Mongols another Divine Wind.)