A sequence of positive integers with 2020 terms is called an FT sequence if each
term after the second is the sum of the previous two terms. For example, if the
first two terms of an FT sequence are 8 and 7, the sequence would begin
8,7,15, 22, 37,.... For some positive integer m, there are exactly 2415 FT sequences
where the first two terms are each less than 2m and the number of odd-valued
terms is more than twice the number of even-valued terms. What is the value of m?

(A) 21
(B) 69
(C) 115
(D) 35
(E) 105