Statement

Given an integer sequence A of length N, answer Q queries. Each query gives k; output the k-th smallest number in the whole sequence.

This is a template problem for the simplest form of overall binary search over the compressed value domain.

Input

N Q
A_1 A_2 ... A_N
k_1 k_2 ... k_Q

Output

Print Q lines, one answer per query.

Constraints

• 1 <= N,Q <= 2 * 10^5
• -10^9 <= A_i <= 10^9
• 1 <= k_i <= N