Sultan's game

 

One day the sultan's most trusted vizier died in battle. Sultan wants to choose a vizier from his soldiers. But it was hard choice for Sultan to select just one man from available N . So Sultan decides to prepare such a game that will help him to choose new vizier. First of all Sultan asks to his favorite soldiers to take a unique number (from 1 to N) and after he enumerates all his soldiers with remaining unique numbers. The rules of Sultan`s game is simple: he arrange soldiers by their numbers in increasing order. Then he eliminates all soldiers whom were standing in 1, 3, 5… positions. After last soldier in eliminated Sultan rearrange soldiers by using same rule and starts elimination game again. Sultan`s game continues until just one soldiers left un eliminated. So Sultan promotes this soldier to vizier position.

 Input

The number of soldiers (n <10 ^ 7) and the number  sultan's favorite soldiers m (m <= n).

The numbers selected by the sultan's favorite soldiers s [i] (s [i]> = 1 && s [i] <= n).

Output

Print the number which number to be vizier.

Print the game ranked number selected by soldiers from the Sultan's favorite.

Input	Output
6 3 1 5 6	4 1 3 5