Leo prepares more than $400$ cupcakes for a party. Now he can divided all of them equally into $5$ piles. After his pet cat eats one of the cupcakes, he finds that now he can divide the remaining cupcakes equally into $6$ piles. Then, the naughty pet cat eat another one, and Leo divides the remaining cupcakes into $7$ piles. How many cupcakes did Leo make at least at the beginning? Find the sum of the three digits. 
选项为:A:$$10$$  B:$$11$$  C:$$12$$  D:$$13$$  E:$$14$$  请回答其中一个选项.