Longest Common Increasing Subsequence

You are given two sequences of positive integers, $A$ and $B$. A common increasing subsequence is a sequence that appears as a subsequence of both $A$ and $B$ and is strictly increasing, meaning every element is greater than the one before it. (The elements of a subsequence need not be adjacent in the original sequence.) Find the length of the longest common increasing subsequence of $A$ and $B$.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 2000$), the lengths of $A$ and $B$. The second line contains the $n$ elements of $A$, and the third line contains the $m$ elements of $B$, separated by single spaces. Every element is a positive integer not exceeding $10^9$.

Print a single integer: the length of the longest common increasing subsequence of $A$ and $B$. If $A$ and $B$ share no common element, print $0$.