Restaurant Guide

Yoon is building a guide app, UNIST Guide, that recommends restaurants near UNIST. Yoon picked $N$ restaurants and numbered them from $1$ to $N$.

Yoon found rankings from two food critics, Donggyu and Wone, who each ranked all $N$ restaurants. Yoon wants to assign ratings based on these two rankings. A rating is an integer star count from $1$ to $S$, where $S$ is a positive integer. A higher star count means a tastier restaurant.

A rating must not contradict either critic's ranking. That is, if restaurant X has a higher rating than restaurant Y, then X must rank above Y in both critics' rankings. The converse does not need to hold.

Every rating level must also be given to at least $K$ restaurants.

Yoon believes the guide becomes more credible when its information is more detailed, so Yoon wants to split the ratings as finely as possible. In other words, Yoon wants the highest star count $S$ to be as large as possible. When the ratings satisfy all the conditions, what is the maximum number of rating levels?

The first line contains two integers $N$ and $K$, separated by a space, where $N$ is the number of restaurants and $K$ is the minimum number of restaurants for each rating level. ($1\le K\le N\le 200\ 000$)

The second line contains the $N$ restaurant numbers in the order of Donggyu's ranking, from highest to lowest, separated by spaces.

The third line contains the $N$ restaurant numbers in the order of Wone's ranking, from highest to lowest, separated by spaces.

Each restaurant number is an integer from $1$ to $N$, and no number repeats within a line.

Print the maximum number of rating levels that Yoon can achieve when the ratings are split as finely as possible.