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: Wrong Answer)

using System;  
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Gtand031_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var first = Console.ReadLine().Split(' ');
            var N = int.Parse(first[0]);
            var K = int.Parse(first[1]);
            var p = Console.ReadLine().Split(' ').Select(c => int.Parse(c)).ToArray();
            var q = Console.ReadLine().Split(' ').Select(c => int.Parse(c)).ToArray();
            var ret = new int[N];
            for(int i = 0; i<K-2;i++)
            {
                for(int j=0;j<N;j++)
                {
                    ret[p[j]-1] = q[j]; 
                }
                p = q;
                q = ret;
            }
            Console.WriteLine(String.Join(" ", ret));
        }
    }
}