AT_abc386_e [ABC386E] Maximize XOR

You are given a sequence $ A $ of non-negative integers of length $ N $ , and an integer $ K $ . It is guaranteed that the binomial coefficient $ \dbinom{N}{K} $ is at most $ 10^6 $ . When choosing $ K $ distinct elements from $ A $ , find the maximum possible value of the XOR of the $ K $ chosen elements. That is, find $ \underset{1\leq i_1\lt i_2\lt \ldots\lt i_K\leq N}{\max} A_{i_1}\oplus A_{i_2}\oplus \ldots \oplus A_{i_K} $ . About XORFor non-negative integers $ A,B $ , the XOR $ A \oplus B $ is defined as follows: - In the binary representation of $ A \oplus B $ , the bit corresponding to $ 2^k (k \ge 0) $ is $ 1 $ if and only if exactly one of the bits corresponding to $ 2^k $ in $ A $ and $ B $ is $ 1 $ , and is $ 0 $ otherwise. For example, $ 3 \oplus 5 = 6 $ (in binary notation: $ 011 \oplus 101 = 110 $ ). In general, the XOR of $ K $ integers $ p_1, \dots, p_k $ is defined as $ (\cdots((p_1 \oplus p_2) \oplus p_3) \oplus \cdots \oplus p_k) $ . It can be proved that it does not depend on the order of $ p_1, \dots, p_k $ .

The input is given from Standard Input in the following format: > $ N $ $ K $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Print the answer.

### Sample Explanation 1 Here are six ways to choose two distinct elements from $ (3,2,6,4) $ . - $ (3,2) $ : The XOR is $ 3\oplus 2 = 1 $ . - $ (3,6) $ : The XOR is $ 3\oplus 6 = 5 $ . - $ (3,4) $ : The XOR is $ 3\oplus 4 = 7 $ . - $ (2,6) $ : The XOR is $ 2\oplus 6 = 4 $ . - $ (2,4) $ : The XOR is $ 2\oplus 4 = 6 $ . - $ (6,4) $ : The XOR is $ 6\oplus 4 = 2 $ . Hence, the maximum possible value is $ 7 $ . ### Constraints - $ 1\leq K\leq N\leq 2\times 10^5 $ - $ 0\leq A_i