Prove: If $4k+1$ is a Quadratic Nonresidue mod $p$ then $k$ is a Quadratic Residue mod $p$

Question

Prove the following:

Let $p$ be an odd prime. Suppose that $4k+1$ is a quadratic nonresidue $\mod p$. Then $k$ must be a quadratic residue.

My attempt at this was to suppose that $k$ is a quadratic nonresidue and show that $4k+1$ is a quadratic residue in order to get a contradiction, but I find it hard to compute $(4k+1)^\frac{p-1}{2}$ in order to use Euler's criterion.