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.

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.)