[POI2010] MOT-Monotonicity 2

This task is a harder version of task Monotonicity from the third stage of 17th Polish OI. It wasn't used in the contest itself. For an integer sequence  we define its monotonicity scheme as the sequence  of symbols ,  or . The symbol  represents the relation between  and . For example, the monotonicity scheme of the sequence  is . We say that an integer sequence  with monotonicity scheme , realizes another monotonicity scheme  if for every  it holds that . In other words, the sequence  can be obtained by repeating the sequence  and removing appropriate suffix from that repetition. For example, the sequence  realizes each and every one of the following schemes:     as well as many others. An integer sequence  and a monotonicity scheme  are given. Your task is to find the longest subsequence  () of the former that realizes the latter. 给出N个正整数a[1..N]，再给出K个关系符号（>、<或=）s[1..k]。 选出一个长度为L的子序列（不要求连续），要求这个子序列的第i项和第i+1项的的大小关系为s[(i-1)mod K+1]。 求出L的最大值。 感谢@cn：苏卿念 提供spj

The first line of the standard input holds two integers  and  (, ), separated by a single space, denoting the lengths of the sequences  and monotonicity scheme  respectively. The second input line gives the sequence , i.e, it holds  integers  separated by single spaces (). Finally, the third lines gives the monotonicity scheme , i.e., it holds  s…

In the first line of the standard output your program should print out a single integer , the maximum length of a subsequence of  that realizes the scheme . In the second line it should print out any such subsequence , separating its elements by single spaces.

7 3
2 4 3 1 3 5 3
< > =

6
2 4 3 3 5 3

$1 \le n \le 500000$，$1 \le k \le 500000$，$1 \le a_i \le 10^6$，$s_j \in \{<, >, =\}$