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.