Farmer John's cows are standing in a line. The -th cow from the left has label . 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 times:
The sequence of cows currently in positions from the left reverse their order. Then, the sequence of cows currently in positions from the left reverse their order.
After the cows have repeated this process exactly times, output the label of the -th cow from the left for each .
The first line of contains and . The second line contains and , and the third line contains and .
On the -th line of output, print the label of the -th cow from the left at the end of the exercise routine.
Initially, the order of the cows is from left to right. After the first step of the process, the order is . After the second step of the process, the order is . Repeating both steps a second time yields the output of the sample.