Problem Statement

You are given N non-negative integers A_1, A_2, ..., A_N and another non-negative integer K.
For a integer X between 0 and K (inclusive), let f(X) = (X XOR A_1) + (X XOR A_2) + ... + (X XOR A_N).
Here, for non-negative integers a and b, a XOR b denotes the bitwise exclusive OR of a and b.
Find the maximum value of f.

What is XOR?
The bitwise exclusive OR of a and b, X, is defined as follows:

• When X is written in base two, the digit in the 2^k'$s place (k \geq 0)$ is 1 if, when written in base two, exactly one of A and B has 1 in the 2^k's place, and 0 otherwise.

For example, 3 XOR 5 = 6. (When written in base two: 011 XOR 101 = 110.)

Input

Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N

Output

Print the maximum value of f.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $0 \leq K \leq 10^{12}$
• $0 \leq A_i \leq 10^{12}$

Sample Input 1

3 7
1 6 3

Sample Output 1

14

The maximum value is: f(4) = (4 XOR 1) + (4 XOR 6) + (4 XOR 3) = 5 + 2 + 7 = 14.

Sample Input 2

4 9
7 4 0 3

Sample Output 2

46

Sample Input 3

1 0
1000000000000

Sample Output 3

1000000000000

见题面 Input 部分

见题面 Output 部分