101173: [AtCoder]ABC117 D - XXOR
Memory Limit：256 MB
Time Limit：2 S
Judge Style：Text Compare
Creator：
Submit：0
Solved：0
Description
Score : $400$ points
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 $101 = 110$.)
Constraints
- All values in input are integers.
- $1 \leq N \leq 10^5$
- $0 \leq K \leq 10^{12}$
- $0 \leq A_i \leq 10^{12}$
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 $f$.
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