Description

pigstd now has $n$ cases of cola. The $i$-th case is labeled with a positive integer $a_i$.

If pigstd's smartness value is a non-negative integer $x$, then for the $i$-th case of cola, if $(a_i \oplus x) \le k$, pigstd can drink this case of cola.

Now pigstd tells you $k$ and the sequence $a$. You may choose pigstd's smartness value $x$ so that the number of cola cases he can drink is maximized. Find this maximum value.

Input Format

The first line contains two integers $n$ and $k$, separated by spaces.

The next $n$ lines each contain one integer $a_i$, indicating the number labeled on the $i$-th case of cola.

Output Format

Output one positive integer in a single line, indicating the maximum number of cola cases that pigstd can drink.

3 5
2
3
4

3

4 625
879
480
671
853

4

Hint

Hint

pigstd's smartness value $x$ can be $0$.

Sample Explanation

Sample 1: It is easy to construct that when $x = 0$, he can drink all colas.

Sample 2: It is easy to construct $x = 913$, and he can drink all colas.

The sample explanation is not necessarily the only way.

Constraints

This problem uses bundled testdata.

• Subtask 1 (29 points): $1 \le n, k, a_i \le 1000$.

• Subtask 2 (1 points): $a_i \le k$.

• Subtask 3 (70 points): No special restrictions.

For all data, it is guaranteed that $1 \le n, k, a_i \le 10^6$.

$\oplus$ denotes XOR. If you do not know what XOR is, please click here.

Translated by ChatGPT 5