GCD Summation

For an array $A$ of length $N$, we define $f(A)$ to be the sum of [GCD](https://en.wikipedia.org/wiki/Greatest_common_divisor)s of its adjacent elements, i.e. $$ f(A) = \sum_{i=1}^{N-1} \gcd(A_i, A_{i+1}) $$ --- You are given two integers $N$ and $K$. Find any array $A$ of length $N$, consisting of **distinct integers** between $1$ and $10^9$, such that $f(A) = K$. If multiple valid arrays