Pikachu loves battling with other Pokemon. This time he has a team of $$ N $$ Meowstic to fight, $$i^{th}$$ of which has strength $$ a_i $$. He wants to fight with all of them $$K $$ times. Team Meowstic came to know about this and now they have devised a strategy to battle against the mighty Pikachu.

All the $$N$$ Meowstic stand in a straight line numbered from $$1$$ to $$N$$. Before every round of battle, they simultaneously use a move, called Helping Hand. It changes the attacking power of Team Meowstic as follows:

The attacking power of first Meowstic remains $$ a_1 $$.
The attacking power of remaining Meowstic changes as $$ a_i = a_i | a_{i-1} $$ where $$ 2 \le i \le N $$ and $$ A | B $$ represents the bitwise OR of $$ A $$ and $$ B $$

For example, if the current attacking powers are $$ [2, 1, 4, 6, 3] $$, after using the Helping Hand, the powers change to $$ [2, 1|2, 4|1, 6|4, 3|6] $$, or $$ [2, 3, 5, 6, 7] $$.

Help Pikachu by finding the attacking powers of all Meowstic when he fights each of them for the last time, that is, for the $$K^{th}$$ round.

Note that, the influence of Helping Hand remains forever, and attacking powers DO NOT revert back after any round.

Constraints:

\(1\le N\le 10^5\)
\(0\le K\le 10^9\)
\(0\le a_i < 2^{30}\)

Input format:

First line contains two space separated integers, $$ N $$ and $$ K $$
Second line contains $$ N $$ space separated integers, the $$ i^{th} $$ of which is $$ a_i $$

Output format:

Output a single line containing $$ N $$ integers, the $$ i^{th} $$ of which is $$ a_i $$ after the last round