I'm learning modular exponentiation with Chinese remainder theorem.


I found a great answer from below
[http://crypto.stackexchange.com/questions/5296/how-can-i-use-eulers-totient-and-the-chinese-remainder-theorem-for-modular-expon][1]

But I can't understand the last step of construction from $C_p$ and $C_q$ very well. Can someone explain it to me? Moreover, if I make $N = 55 = 11 \times 5$ instead of $5 \times 11$, that last step fails to give correct answer. 

The last step:
$$M^e \bmod{pq}= C_q+q((C_p−C_q) \bmod p)$$

 


  [1]: http://crypto.stackexchange.com/questions/5296/how-can-i-use-eulers-totient-and-the-chinese-remainder-theorem-for-modular-expon