Different path for grid move (part 3)
Since you never use r you can shift it down by one and call it _ (the customary unused variable in Python).

def grid_move_v2(rights, ups):
    cur = [1] * (ups + 1)
    for _ in range(rights):
        for u in range(1, ups+1):
            cur[u] = cur[u] + cur[u-1]
    return cur[-1]