The Intervals

Time Limit: 1 Second    Memory Limit: 32768 KB

Cantor, the famous mathematician, was working on a problem about intervals.

Let's start from a line segment of unit length. Remove its middle 1/3.

Now remove the middle 1/3's from the remaining two segments.
Now remove the middle 1/3's from the remaining four segments.
Now remove the middle 1/3's from the remaining eight segments.
Now remove ... well, you get the idea.

If you could continue this procedure through infinitely many steps, what would you have left?

Now he assigns the following task to you. (He asked me to pass his assignment to you last night.)

Given two arrays of numbers {A(n)} and {B(m)}. For each B(i) in {B(m)}, find 2 numbers a and b from {A(n)}, such that B(i) is in [a,b) and b-a<=|b'-a'| for all a' and b' from {A(n)} such that [a',b') contains B(i).

Input

There are several test cases.

In each test case, the first line gives n and m.

The second line contains n numbers, which are the elements of {A(n)}.

The third line contains m nubmers, which are the elements of {B(m)}.

Output

For each B(i) in {B(m)}, output a line containing the interval [a,b).

If there is no such interval, output "no such interval" instead.

Print a blank line after each test case.

Sample Input

3 3
10 20 30
15 25 35

Sample Output

[10,20)
[20,30)
no such interval

Submit

Source: ZOJ Monthly, November 2003