[ABC117D] XXOR

ID: 810

传统题

2000ms

1024MiB

难度: 4

上传者:

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 $101 = 110$ .)

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $A_2$ $...$ $A_N$

Print the maximum value of $f$ .

3 7
1 6 3

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

4 9
7 4 0 3

1 0
1000000000000

1000000000000