Let $M$ is a four digit positive interger. Write $M$ backwards and get a new number $N$.(e.g $M=1234$ then $N=4321$) Let $C$ is the sum of every digit of $M$. If $M,N,C$ satisfies (i)$d=\gcd(M-C,N-C)$ and $d<10$ (ii)$\dfrac{M-C}{d}=\lfloor\dfrac{N}{2}+1\rfloor$ (1)Find $d$. (2)If there are "m(s)" $M$ satisfies (i) and (ii), and the largest $M$=$M_{max}$. Find $(m,M_{max})$