Given a multiset of integers having cardinality n, find its Supreme Subset.
A supreme subset of a given multiset is one of its subsets in which -

1. if any two elements $i, j$ are chosen from subset, $|i - j|$ is divisible by m, where x represents absolute value of x.
2. it has the highest cardinality/size among all candidate subsets satisfying condition 1.
3. If there are multiple subsets satisfying above 2 conditions, the supreme subset is the one which is smallest by set comparison.

Finding order by set comparison - Given two sets of the same size, the smaller one is defined to be the one which is lexicographically smaller when both sets are arranged in non-decreasing order, for example, the set {3,2,1} is smaller than {3,2,2}.

Input:
The first line of the input contains 2 integers, $n, m$, as specified in the problem statement.
The second line contains n integers, representing the multiset A.

Output:
First line should have 1 integer, k, representing cardinality of the Supreme Subset.
Second line should have k members of the supreme subset in sorted order.

Constraints:
$1 \le n \le 10^5$
$1 \le m \le 10^9$
$1 \le A_i \le 10^9$