Megavirus

A hacker built a megavirus. Every copy of the virus has its own number, and the very first copy is numbered $0$. Every minute a new generation of viruses is created. A virus numbered $i$ in generation $k$ produces two children in generation $k + 1$, numbered $2 \cdot i$ and $2 \cdot i + 1$. These two newly created viruses $2 \cdot i$ and $2 \cdot i + 1$ are called the children of virus $i$ from generation $k$. Virus $v$ together with its children, its children's children, and so on are called the descendants of $v$ (virus $v$ is also counted among its own descendants), and $v$ is called their ancestor; in particular, every virus is an ancestor of itself. Generation numbers start from $0$. The viruses that live in each generation are:

• generation $0$: virus $0$
• generation $1$: viruses $0$, $1$
• generation $2$: viruses $0$, $1$, $2$, $3$
• generation $3$: viruses $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$
• ...

Given one generation number and the numbers of several viruses from that generation, compute the largest generation number that contains a common ancestor of all the given viruses, and print it.

The first line contains two integers $k$ and $n$ separated by a space. $k$ ($1 \le k \le 512$) is the generation number, and $n$ ($1 \le n \le 150$) is the number of viruses to read. Each of the next $n$ lines contains the number of one virus. Since every virus belongs to generation $k$, each number is an integer between $0$ and $2^k - 1$ inclusive.

Print, on a single line, the largest generation number that contains a common ancestor of all the viruses.