Swapity Swap

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

• The sequence of cows currently in positions $a_1,...,a_2$ from the left reverse their order. Then, the sequence of cows currently in positions $b_1....,b_2$ 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 $i(1\le i\le n)$.

Input

The first line of contains $n(1\le n\le 100)$ and $k(1\le k\le 10^9)$. The second line contains $a_1$ and $a_2(1\le a_1<a_2\le n)$, and the third line contains $b_1$ and $b_2(1\le b_1<b_2\le n)$.

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.

Examples

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.