Swapity Swap

문제

Farmer John's $NN$ cows ($1\le N\le 1001\backslash le\; N\backslash le\; 100$) are standing in a line. The $ii$th cow from the left has label $ii$, for each $1\le i\le N1\backslash le\; i\backslash le\; N$.

Farmer John has come up with a new morning exercise routine for the cows. He tells them to repeat the following two-step process exactly $KK$ ($1\le K\le {10}^{9}1\backslash le\; K\backslash le\; 10^9$) times:

1. The sequence of cows currently in positions $A_1\dots A_{2}A\_1\; \backslash ldots\; A\_2$ from the left reverse their order ().
2. Then, the sequence of cows currently in positions $B_1\dots B_{2}B\_1\; \backslash ldots\; B\_2$ from the left reverse their order ().

After the cows have repeated this process exactly $KK$ times, please output the label of the $ii$th cow from the left for each $1\le i\le N1\backslash le\; i\backslash le\; N$.

입력

The first line of input contains $NN$ and $KK$. The second line contains $A_{1}A\_1$ and $A_{2}A\_2$, and the third contains $B_{1}B\_1$ and $B_{2}B\_2$.

출력

On the $ii$th line of output, print the label of the $ii$th cow from the left at the end of the exercise routine.

힌트

Initially, the order of the cows is $[1,2,3,4,5,6,7][1,2,3,4,5,6,7]$ from left to right. After the first step of the process, the order is $[1,5,4,3,2,6,7]\mathrm{.}[1,5,4,3,2,6,7].$ After the second step of the process, the order is $[1,5,7,6,2,3,4][1,5,7,6,2,3,4]$. Repeating both steps a second time yields the output of the sample.

7 2
2 5
3 7

1
2
4
3
5
7
6