Given an array of length ~N~ and ~Q~ queries, print the closest number to the value given in each query.

Input Specification

The first line will contain integer ~N~ ~(1 \leq N \leq 10^5)~ and ~Q~ ~(1 \leq Q \leq 10^5)~, the length of the array and the number of queries, respectively. The next line will contain ~N~ integers, the values in the array. It is guaranteed that these values will be smaller than ~10^9~. The next ~Q~ lines will contain an integer ~a~ ~(1 \leq a \leq 10^9)~, the value that you are to find the closest number to.

Output Specification

For each query, one integer that is either the integer in the array that is closest to ~a~. If there are multiple numbers that have the same distance from ~a~ print the largest one.

Subtasks

Subtask 1 (50%)

~N,Q \leq 10^3~

Subtask 2 (50%)

No further constraints.

Sample Input 1

5 5
2 3 6 9 10
1
2
6
13
9

Sample Output 1

2
2
6
10
9