The set $B = \left( \begin{bmatrix} 1 \ -2 \ -1 \end{bmatrix}, \begin{bmatrix} 4 \ -9 \ -5 \end{bmatrix}, \begin{bmatrix} -3 \ 6 \ 2 \end{bmatrix} \right)$ is a basis for $\mathbb{R}^3$. Find the coordinates of the vector $\vec{u} = \begin{bmatrix} 16 \ -31 \ -10 \end{bmatrix}$ with respect to the basis $B$.