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Competitions

Swapity Swap

Farmer John's n cows are standing in a line. The i-th cow from the left has label i (1in). 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 k times:

• The sequence of cows currently in positions a1 . . . a2 from the left reverse their order. Then, the sequence of cows currently in positions b1 . . . b2 from the left reverse their order.

After the cows have repeated this process exactly k times, output the label of the i-th cow from the left for each i (1in).

Input

The first line of contains n (1n100) and k (1k109). The second line contains a1 and a2 (1a1 < a2n), and the third contains b1 and b2 (1b1 < b2n).

Output

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

Hint

Initially, the order of the cows is [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]. After the second step of the process, the order is [1, 5, 7, 6, 2, 3, 4]. Repeating both steps a second time yields the output of the sample.

Time limit 1 second
Memory limit 128 MiB
Input example #1
7 2
2 5
3 7

Output example #1
1
2
4
3
5
7
6

Source 2020 USACO February Bronze