GATE EC 2021 Set 1 Q5 — Discrete-time Signals

Consider two $16$-point sequences $x\left [ n \right ]$ and $h\left [ n \right ]$. Let the linear convolution of  $x\left [ n \right ]$ and $h\left [ n \right ]$ be denoted by $y\left [ n \right ]$, while $z\left [ n \right ]$ denotes the $16$-point inverse discrete Fourier transform $\text{(IDFT)}$ of the product of the $16$-point $\text{DFTs}$ of $x\left [ n \right ]$ and $h\left [ n \right ]$. The value(s) of $k$ for which $z\left [ k \right ]=y\left [ k \right ]$ is/are