You are given an array A that contains N elements and an integer K that represents the value of a non-empty subsequence $B_1, B_2, \ldots, B_m$ of $A$ is defined as $(B_1 \land K) \land (B_2 \land K) \land \ldots \land (B_m \land K) \cdot gcd\ (B_1, B_2, \ldots, B_m)$ (where $\land$ is the XOR operator). Determine the maximum value of any non-empty subsequence in the given array.

For example, if the elements of array $A$ is $[2,\ 4,\ 6]$ and $K$ is $6$, then the maximum value is achieved you select the subsequence $[2, 4]$. In this case, the value of the subsequence will be $((2 \land 6) \land (4 \land 6)) * gcd\ (2, 4) = 6 * 2 = 12$.

Note: A sequence $b$ is a subsequence of a sequence $a$ if $b$ can be obtained from $a$ by deleting several (possibly zero) elements. For this question, assume that if the sequence has a single element, then the gcd is the element itself.

Input format

• First line: Two integers $N$ and $K$ ($1 \le N, K \le 10^5$), where $N$ denotes the number of elements in the array
• Second line: $N$ integers $A_1, A_2, \ldots, A_n\ (1 \le A_i \le 10^5)$ that denote the elements of the array

Output format

Print the maximum value of any non-empty subsequence of the given array.