Let the line $L$ pass through $(1,1,1)$ and intersect the lines $\dfrac{x-1}{2} = \dfrac{y+1}{3} = \dfrac{z-1}{4}$ and $\dfrac{x-3}{1} = \dfrac{y-4}{2} = \dfrac{z}{1}$. Then, which of the following points lies on the line $L$?