TxO Math Bowl 2024 - Guts Contest - Set 4 Problem 1

A cat walks from (0,0) to (11,7) on the coordinate plane in 20 steps. On each step, the cat walks one unit in the positive or negative, x or y direction (so it can walk in all 4 cardinal directions). Let m be the number of possible paths that the cat could take if it cannot turn 180^\circ while changing direction. Compute the number of positive factors of m.