Speed of light paradox

Hi, there is something I can't understand:

Consider a stationary observer at A. Now consider an observer B in a train that moves with constant velocity v with respect to A. In the train, B tries to measure the speed of light using an empty tube of length L₀ (proper length as measured by B). He sends a light signal at extremity E, the signal reaches extremity F (where a mirror exists) and return back to the extremity E. B measure this duration T₀ (proper period as measured by B).

Now B measure the speed of light as:

C_B = 2L₀/T₀

Now according to A the length of the tube is contracted and the time is dilated, so he measure the speed of light as:

C_A = 2L/T = (2L₀/γ)/(γT₀) = (L₀/T₀)/(γ^2) = C_B/(γ^2)

which is different from the value measure by B (divided by Gamma squared)

thanks harrylin, what I was thinking is from post #1, d=2Lo/Y and t=YTo which gave c as "divided by gamma squared".
This was wrong from the beginning, the length in the stationary frame is longer than the moving length Lo as you state, confusing because each is moving relative to the other. And also the time is YTo in the "stationary" frame, longer.
I guess this all makes sense, I just get confused about time dilation/expansion using t in different ways it seems to me, sometime an interval, sometimes ticks. Oh well, will come together sooner or later.
Thanks.