Let $$(2,3)$$  be the largest open interval in which the function $$f(x)=2\log_e(x-2)-x^2+ax+1$$ is strictly increasing and  $$(b,c)$$  be the largest open interval in which the function $$g(x)=(x-1)^3(x+2-a)^2$$ is strictly decreasing. Then  $$100(a+b-c)$$  is equal to:

A

420

B

360

C

160

D

280