Bitcoin Is God and I Am Invincible

Time limit1sMemory limit1024 MB

Summary

Choose exactly M values from N given numbers, repetition allowed, to maximize the bitwise XOR of the chosen values.

Level: Medium6 of 10
Topics: Dynamic programming, Bit manipulation, Brute force
Solved: No attempts yet

Problem

Chanho, who has four years of experience with coins and knows charts inside out, came up with the following formula that predicts the absolute value of the next monthly candle from the previous $N$ monthly candles.

(Absolute value of the next monthly candle) = the maximum over all choices of $M$ of the previous $N$ monthly candles, repetition allowed, of the bitwise xor of their absolute values

Given $N$ , $M$ , and the previous monthly candles $A_i$ , find the absolute value of the next monthly candle.

Input

The first line gives $N$ and $M$ .

The second line gives $A_1, A_2, \cdots, A_N$ .

Output

Print the absolute value of the next monthly candle.

Constraints

$1 \leq M \leq N \leq 100$
$0 \leq |A_i| < 2^{10}$

Examples1

Example 1
Input
```
3 2
-1 2 3
```
Expected output
```
3
```