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≤105) and q (1≤q≤105). The next line contains N space separated integers, ai (0≤ai≤109), forming this array. Next q lines will contain the value of x (0≤x≤109).
Output
For each x you have to print a line containing the minimum value of z.