# Matching

Time limit: 5 seconds
## Problem

A lot of text editors have an auto-match ability.
When you highlight an opening or
closing parenthesis, i.e., '(' or ')',
the matching parenthesis will be highlighted automatically.
This problem requires you to do something similar.
## Input

The input consists of a number of test cases.

For each test case, the first line contains
two integers *1 <= n <= 1,000,000*
and *1 <= m <= 1,000*.
The next line is a list of *n* parentheses.
The parentheses are balanced.
Then there are *m* lines, each
containing a single integer *q*, which is a query asking
for the parenthesis that matches the *q*-th parenthesis
in the list.

The last test case starts with "0 0" and
no further lines. Do not process this case.
## Output

For each query *q*, output an integer *i* on a single line
such that the *i*-th parenthesis matches
the *q*-th parenthesis.
Output a blank line after each test case.
## Sample Input

20 5
((((((()()()()))))))
1
19
5
7
10
30 4
()()()()()((((((()()()()))))))
1
2
11
15
0 0

## Sample Output

20
2
16
8
9
2
1
30
26

## Author

Angela Siu