Make It One

You're given two positive integers $L$ and $R$ ($L \lt R$). Let $N = R-L+1$. Consider the array $A = [L, L+1, L+2, \ldots, R]$ of length $N$ that contains every integer from $L$ to $R$ exactly once, in order. Find *any* array $B$ of length $N$ such that: - Every integer from $L$ to $R$ appears exactly once in $B$; and - For each $1 \leq i \leq N$, $\gcd(A_i, B_i) = 1$. If no such $B$ exists,