The singular abundance conjecture for klt varieties with numerically trivial canonical class

Let $X$ be a normal projective klt variety with $H^1(X,\mathcal O_X)=0$ and $K_X\sim_{\mathbb Q}0$, and let $L$ be a nef divisor. Singular abundance conjecture. Then $L$ is semiample. This is the singular analogue of the abundance conjecture for smooth projective manifolds with trivial canonical class.