Maximizing Drank Coke Boxes

pigstd has n boxes of coke. The i-th box is labeled with a positive integer \(a_i\). pigstd's cleverness value is a non-negative integer \(x\). For each box, if \(a_i \oplus x \le k\), then pigstd can drink from that box. You are given \(k\) and the sequence \(a\). Determine the maximum number of boxes pigstd can drink from by choosing an appropriate \(x\).

inputFormat

The first line contains two integers \(n\) and \(k\). The second line contains \(n\) positive integers \(a_1, a_2, \dots, a_n\), separated by spaces.

outputFormat

Output a single integer representing the maximum number of boxes pigstd can drink from.

sample

3 2
1 2 3

3