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_yK (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:

• 2 ≤ N, K ≤ 2 · 10⁴
• 0 ≤ M ≤ 2 · 10⁴
• 0 ≤ B_i ≤ 10⁹
• N, M, K ≤ 100 in test data worth 20% of all points
• M = 0 in test data worth 20% of all points