SOLVE
LATER
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:
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:
Input format:
Output format:
Battle 1:
$$ a_1 = 1, a_2 = 1 | 2 = 3, a_3 = 2 | 3 = 3, a_4 = 3 | 4 = 7, a_5 = 4 | 5 = 5 $$
Battle 2:
$$ a_1 = 1, a_2 = 1 | 3 = 3, a_3 = 3 | 3 = 3, a_4 = 3 | 7 = 7, a_5 = 7 | 5 = 7 $$
Battle 3:
$$ a_1 = 1, a_2 = 1 | 3 = 3, a_3 = 3 | 3 = 3, a_4 = 3 | 7 = 7, a_5 = 7 | 7 = 7 $$