Essa has presented you with one of his 3 legendary problems, you'll be given an array $A$ of $n$ non-negative integers, an integer $d$, and he asks you to find $m$, defined as:

The size of the largest subset of elements $S$ you can pick from $A$ such that the following three conditions are satisfied:

• The bitwise AND of all of the elements in the chosen set $S$ is equal to $d$ $(S_1 \; \& \; S_2 \; \& \; S_3 \; \& \; \ldots \; \& \; S_m = d)$
• The bitwise OR of all of the elements in the chosen set $S$ is equal to $d$ $(S_1 \; | \; S_2 \; | \; S_3 \; | \; \ldots \; | \; S_m = d)$
• The bitwise XOR of all of the elements in the chosen set $S$ is equal to $d$ $(S_1 \; \oplus \; S_2 \; \oplus \; S_3 \; \oplus \; \ldots \; \oplus \; S_m = d)$

The first line will contain two integers $n$ and $d$ $(1 \le n \le 2 * 10^5, 0 \le d \le 10^9)$.

The second line will contain $n$ space-separated integers, the contents of the array $(0 \le A_i \le 10^9)$.

If there's no such subset of elements, print the integer $0$. Otherwise, print the maximum possible size of a subset $S$ that satisfies the given conditions.