Farmer John's NN cows (1≤N≤1001≤N≤100) are standing in a line. The iith cow from the left has label ii, for each 1≤i≤N1≤i≤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≤K≤1091≤K≤109) times:

1. The sequence of cows currently in positions A1**…A2A1…A2 from the left reverse their order (1≤A1<A2≤N**1≤A1<A2≤N).
2. Then, the sequence of cows currently in positions B1**…B2B1…B2 from the left reverse their order (1≤B1<B2≤N**1≤B1<B2≤N).

After the cows have repeated this process exactly KK times, please output the label of the iith cow from the left for each 1≤i≤N1≤i≤N.

SCORING:

• Test cases 2-3 satisfy K≤100K≤100.
• Test cases 4-13 satisfy no additional constraints.

INPUT FORMAT (file swap.in):

The first line of input contains NN and KK. The second line contains A1A1 and A2A2, and the third contains B1B1 and B2B2.

OUTPUT FORMAT (file swap.out):

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

SAMPLE INPUT:

7 2
2 5
3 7

SAMPLE OUTPUT:

1
2
4
3
5
7
6

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].[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.