Find unitary matrix $Q$ such that $U=Q*V$ with $U$ given and first column of $V$ given

Question

Given all entries of $n \times m$ complex matrix $U$,and given the first column of $n \times m$ complex matrix $V$, find a unitary matrix $Q$ such that $U=Q*V$ while the first column of $V (v_1)$ is known.

I wonder whether there is any simple method to compute $Q$? Thanks in advance.