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