Kevin thinks that array A is beautiful if

It contains N positive integers.
It doesn't contain any bad numbers.
There doesn't exist any number x and tuple (y₁, y₂, ..., y_K) such that A_x = A_y₁ · A_y₂ · ... · A_{y_K} (y_i < x).

Kevin knows M bad numbers B_i. Kevin also knows that 1 isn't a bad number. Now he wants to find lexicographically smallest beautiful array.

Input format:

The first line of the input contains three numbers N, K, M. The next line contains M integers - B_i.

Output format:

Output N integers - lexicographically smallest beautiful array.

Constraints: