Let $y[n]=\frac{1}{\alpha} y[n-1]+x[n]$, where $\alpha>1$ and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is initially at rest. If $x[n]=\delta[n-p]$ where $p>10$, the value of $y[p+1]$ is
- $0$
- $1$
- $\frac{1}{\alpha}$
- $\frac{1}{\alpha^{2}}$
