J. Never Add Up to X
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Máximo really enjoys collecting plushies. He has $$$N$$$ plushies, and he assigned a beauty value to each of them, which is a positive integer. He wants to arrange them all on his shelf in a row.

Since Máximo believes that the number $$$X$$$ brings bad luck, he wants to organize them on his shelf in such a way that there are no two plushies whose sum of beauties equals $$$X$$$ and that are adjacent in the row.

Can Máximo achieve his goal? If the answer is yes, you should indicate how he can do it.

Input

A line with two integers $$$N$$$ and $$$X$$$ $$$(2 \leq N \leq 3 \cdot 10^5, 1 \leq X \leq 10^9)$$$, the number of plushies Máximo has and the number he believes brings bad luck.

Then a line with $$$N$$$ integers $$$B_1, B_2, \ldots, B_N$$$ $$$(1 \leq B_i \leq X)$$$, the beauty values of each of Máximo's plushies.

Output

If Máximo cannot achieve his goal, a single line containing "*".

Otherwise, a single line containing the beauties of the $$$N$$$ plushies, in the order in which Máximo places them on his shelf.

If there are multiple solutions, any of them will be accepted.

Examples
Input
6 7
1 2 5 4 6 7
Output
1 7 5 4 2 6
Input
2 5
2 3
Output
*
Input
3 10
2 6 2
Output
2 6 2
Note

In the first example, if Máximo places the plushies in such a way that their beauties are $$$[1, 7, 5, 4, 2, 6]$$$, then the sums of adjacent plushies are $$$[8, 12, 9, 6, 8]$$$. None of these numbers is equal to $$$X=7$$$.

In the second example, Máximo cannot achieve his goal, as the only ways to arrange them would be $$$[2, 3]$$$ and $$$[3, 2]$$$, and $$$2 + 3 = 3 + 2 = 5 = X$$$.

In the third example, any arrangement of the plushies is valid.