This problem is a Mooshak version of a CSES problem.

[PC010] Concert Tickets

There are \(n\) concert tickets available, each with a certain price. Then, \(m\) customers arrive, one after another.

Each customer announces the maximum price they are willing to pay for a ticket, and after this, they will get a ticket with the nearest possible price such that it does not exceed the maximum price.

Input

The first input line contains integers \(n\) and \(m\): the number of tickets and the number of customers.

The next line contains \(n\) integers \(h_1,h_2,\ldots,h_n\): the price of each ticket.

The last line contains \(m\) integers \(t_1,t_2,\ldots,t_m\)​: the maximum price for each customer in the order they arrive.

Output

Print, for each customer, a line with the price that they will pay for their ticket. After this, the ticket cannot be purchased again.

If a customer cannot get any ticket, print -1.

Constraints

• \( 1 \leq n,m \cdot 10^5 \)
• \( 1 \leq h_i, t_i \leq 10^9 \)

5 3
5 3 7 8 5
4 8 3

3
8
-1