Password Creation

Hyangbin works as a security officer in the computer lab at Sogang University. One day he receives an email. The email says that abnormal login attempts on the server administrator account have been detected, and the attached file contains the list of passwords used in the login attempts so far. The password for the server administrator account can be any integer from $0$ to $N$.

The safety distance between two passwords is defined as the number of positions where the two passwords differ in binary representation. For example, $3$ in binary is $0011$ and $8$ in binary is $1000$. They differ in $3$ positions, so the safety distance between $3$ and $8$ is $3$.

The safety level of a password is defined as the minimum of its safety distances to every password used in the login attempts so far. For example, suppose the passwords used so far are $3$ and $4$. For a new password $8$, the safety distance between $3$ and $8$ is $3$, and the safety distance between $4$ and $8$ is $2$, so the safety level of $8$ is $2$.

To delay the hacker from finding out the password as long as possible, Hyangbin wants to change the administrator account password currently in use so that its safety level is as high as possible. Find the safety level of the password with the highest safety level.

The first line contains the integer $N$, the maximum value of the administrator account password. ($0 \leq N \leq 1\ 000\ 000$)

The second line contains the integer $M$, the number of passwords used in the login attempts. ($1 \leq M \leq 100\ 000$)

The third line contains the integers $p_1, p_2, \cdots, p_M$, the passwords used in the login attempts. ($0 \leq p_i \leq N$)

Print the safety level of the password with the highest safety level.