For a positive integer $n$, let's denote function $f(n,m)$ as the $m$-th smallest integer $x$ that $x>n$ and $\gcd(x,n)=1$. For example, $f(5,1)=6$ and $f(5,5)=11$.
You are given the value of $m$ and $(f(n,m)-n)\oplus n$, where ``$\oplus$'' denotes the bitwise XOR operation. Please write a program to find the smallest positive integer $n$ that $(f(n,m)-n)\oplus n=k$, or determine it is impossible.