Vhdl implementation of Reed Solomon encoder

In the above block Diagram, we are using Galois arithmetic to form an 
encoder. here the field generator polynomial(p(x)) and code generator 
polynomial(g(x))are taken as follows,
We have used p(x)= x4+x+1
and
g(x)=(x+1)(x+2)(x+4)(x+8)
= x^4+15x^3+3x^2+x+12
The message polynomial is taken as:
M(x) = x^14 +2x^13 +3x^12 +4x^11 +5x^10 +6x^9 +7x^8 +8x^7 +9x^6 +10x^5 
+11x^4 + 12x^3 +13x^2 +14x +15

Then this is multiplied by x4  to give:

x^18 + 2x^17 + 3x^16 + 4x^15 + 5x^14 + 6x^13 +7x^12 +8x^11 +9x^10 +10x^9 
+11x^8 +12x^7 +13x^6 +14x^5 +15x^4
 to allow for spacing for parity symbols.

This is then divided by (x+1)(x+2)(x+4)(x+8) to produce the parity 
symbols
as remainder.
So can you tell me what will be the remainder that we will get here!!
Please Help!!!