OPM 1996 Problem 6

In a regular polygon with $134$ sides, $67$ diagonals are drawn so that exactly one diagonal emerges from each vertex. We call the length of a diagonal the number of sides of the polygon included between the vertices of the diagonal and which is less than or equal to $67$ . If we order the lengths of the diagonals in ascending order, we obtain a succession of $67$ numbers $(d_1,d_2,...,d_{67})$ . It will be possible to draw diagonals such that

a) $(d_1,d_2,...,d_{67})=\underbrace{2 ... 2}_{6},\underbrace{3 ... 3}_{61}$ ?

b) $(d_1,d_2,...,d_{67}) =\underbrace{3 ... 3}_{8},\underbrace{6 ... 6}_{55}.\underbrace{8 ... 8}_{4}$ ?