The solution must start with index $1,$ because choices $2$ and $3$ result in an immediate mismatch. But then, the $\text{A-string}$ is shorter than the $\text{B-string}$, and there is no pair that allows the length of the $\text{A-string}$ to grow faster than that of the $\text{B-string}$. Hence, we cannot create any solution to this problem.
