A8839 | Playing with Permutations

Little Petya likes permutations a lot. Recently his mom has presented him permutation $q_{1},q_{2},...,q_{n}$ of length $n$ .

A permutation $a$ of length $n$ is a sequence of integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=n)$ , all integers there are distinct.

There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length $n$ . Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:

- Before the beginning of the game Petya writes permutation $1,2,...,n$ on the blackboard. After that Petya makes exactly $k$ moves, which are described below.
- During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation $p_{1},p_{2},...,p_{n}$ at the given moment. Then Petya removes the written permutation $p$ from the board and writes another one instead: $p_{q1},p_{q2},...,p_{qn}$ . In other words, Petya applies permutation $q$ (which he has got from his mother) to permutation $p$ .
2. All actions are similar to point 1, except that Petya writes permutation $t$ on the board, such that: $t_{qi}=p_{i}$ for all $i$ from 1 to $n$ . In other words, Petya applies a permutation that is inverse to $q$ to permutation $p$ .

We know that after the $k$ -th move the board contained Masha's permutation $s_{1},s_{2},...,s_{n}$ . Besides, we know that throughout the game process Masha's permutation never occurred on the board before the $k$ -th move. Note that the game has exactly $k$ moves, that is, throughout the game the coin was tossed exactly $k$ times.

Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.

The first line contains two integers $n$ and $k$ ( $1<=n,k<=100$ ). The second line contains $n$ space-separated integers $q_{1},q_{2},...,q_{n}$ ( $1<=q_{i}<=n$ ) — the permutation that Petya's got as a present. The third line contains Masha's permutation $s$ , in the similar format.

It is guaranteed that the given sequences $q$ and $s$ are correct permutations.

If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).