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