XNOR's Rebellion

Competitive programming problems always use only XOR, and XNOR is furious about it. It decides to start a rebellion by gathering $N$ non-negative integers!

XNOR is methodical, so before starting the rebellion it wants to calculate its strength first. Since this is XNOR's rebellion, the strength is the result of applying XNOR to the given numbers in order from the front. Every integer XNOR gathered can be written as an unsigned $B$-bit integer, so XNOR uses XNOR on $B$-bit integers.

A higher strength means a higher chance of success, so XNOR picks one or more of the $N$ numbers to maximize the strength. The order of the chosen numbers cannot be changed.

The first line contains $N$, the number of integers XNOR gathered, and $B$, the number of bits XNOR uses, separated by a space. ($1\le N\le 200\,000$; $1\le B\le 60$)

The second line contains the $N$ non-negative integers $A_1,A_2,\ldots,A_N$ in decimal form, separated by spaces. ($0\le A_{i}<2^B$)

Print the maximum strength of the rebellion that XNOR can produce on the first line.

The bitwise XNOR of two numbers converts both to binary and compares each bit. The result bit is $1$ if the two bits match and $0$ if they differ. For example, $1100_{(2)}\text{ XNOR } 0110_{(2)}=0101_{(2)}$.