Allen has some apples, and the number of apples is more than $2200$ but less than $2300$. If he distributes them among $12$ children evenly, there will be $11$ apples left. If he distributes them among $13$ children evenly, there will be $7$ apples left.~ If he distributes them among $14$ children evenly, there will be $3$ apples left. Which is the correct range of the number of pens? 
选项为:A:$2530\sim2540$  B:$2540\sim2550$  C:$2550\sim2560$  D:$2570\sim2590$  E:$2580\sim2600$  请回答其中一个选项.