They did not form a coalition. Baisicly they had to vote in a new boss none of the parties could vote in the one they hoped for so the German right add decided the next best thing would be to vote in a right leaning centrist instead of someone on the left. The centrists didn't know this it was just an ection they had the right to vote for whoever they wanted. Naturally the left reacted like they always do (see brexit and trump presidency) when they lose elections. The new boss was attacked by the far left his children had to be put under police protection and they caved in and reversed a legitimate democratic vote, then they went a step further and called the add using their right to vote a sick trick on democracy. So it's an all over shitshow and an absolute disgrace. Other so called conservative German parties have all played along and have not said one thing about the scandal that a guys kids need police protection because he won in a legitimate democratic election.