You are given an array of N integers and q queries. In each query you are given an integer value x. For each x you have to choose a value from the given array. Let, this value be y. Now your task is to find the minimum value of z. Where,

z = max(x, y) - min(x, y).

max(x, y) means maximum value between x and y.

min(x, y) means minimum value between x and y.

Input

First line contains two integers N(1≤N≤10^5) and q (1≤q≤10^5). The next line contains N space separated integers forming this array. Next q lines will contain the value of x.

Constraints

1≤N≤10^5

1≤q≤10^5

0 ≤ integers in array≤10^9

0≤x≤10^9

Output

For each x you have to print a line containing the minimum value of z.

Sample

5 2
2 1 6 4 5
1
3

0
1