Problem:
Score : 1000 points

Problem Statement

For two permutations p and q of the integers from 1 through N, let f(p,q) be the permutation that satisfies the following:

The p_i-th element (1 \leq i \leq N) in f(p,q) is q_i.
Here, p_i and q_i respectively denote the i-th element in p and q.

You are given two permutations p and q of the integers from 1 through N.
We will now define a sequence {a_n} of permutations of the integers from 1 through N, as follows:

a_1=p, a_2=q

a_{n+2}=f(a_n,a_{n+1}) ( n \geq 1 )

Given a positive integer K, find a_K.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq 10^9

p and q are permutations of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:

N K
p_1 ... p_N
q_1 ... q_N

Output

Print N integers, with spaces in between.
The i-th integer (1 \leq i \leq N) should be the i-th element in a_K.

Sample Input 1

3 3
1 2 3
3 2 1

Sample Output 1

3 2 1

Since a_3=f(p,q), we just need to find f(p,q).
We have p_i=i here, so f(p,q)=q.

Sample Input 2

5 5
4 5 1 2 3
3 2 1 5 4

Sample Output 2

4 3 2 1 5

Sample Input 3

10 1000000000
7 10 6 5 4 2 9 1 3 8
4 1 9 2 3 7 8 10 6 5

Sample Output 3

7 9 4 8 2 5 1 6 10 3

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System.Linq;using static System.Console;class K{int[]G=>ReadLine().Split().Select(i=>int.Parse(i)-1).ToArray();int N;int[]X=>new int[N];static void Main()=>new K().Z();void Z(){var I=G;N=I[0]+1;WriteLine(string.Join(" ",C(G,G,I[1]).Select(i=>i+1)));}int[]C(int[]p,int[]q,int K){int[]P=I(p),Q=I(q),x=E(M(q,P,Q,p),K/6),y=I(x);switch(K%6){case 0:return M(x,p,y);case 1:return M(x,q,y);case 2:return M(x,q,P,y);case 3:return M(x,q,P,Q,y);case 4:return M(x,q,P,Q,p,Q,y);default:return M(x,q,P,Q,p,p,Q,y);}}int[]I(int[]a){var c=X;for(var i=0;i<N;i++)c[a[i]]=i;return c;}int[]M(params int[][]l)=>l.Aggregate((a,b)=>{var p=X;for(var i=0;i<N;i++)p[i]=a[b[i]];return p;});int[]E(int[]a,int b){int[]p=X,f=X,l=X;for(var i=0;i<N;i++)if(f[i]<1){int x=i,C=0;while(f[x]<1){l[C++]=x;f[x]=1;x=a[x];}for(var j=0;j<C;j++)p[l[j]]=l[(j+b)%C];}return p;}}