Bobo has a balanced parenthesis sequence of length n
and q questions.
The i-th question is whether P remains balanced after and swapped.
Note that questions are individual so that they have no affect on others.
Parenthesis sequence S is balanced if and only if:
1. S is empty;
2. or there exists *balanced* parenthesis sequence A, B such that S = AB;
3. or there exists *balanced* parenthesis sequence S' such that S = (S').

The input contains at most 30 sets. For each set:
The first line contains two integers n, q ().
The second line contains n characters .
The i-th of the last q lines contains 2 integers  ().

For each question, output "`Yes`" if P remains balanced, or "`No`" otherwise.

4 2
(())
1 3
2 3

No
Yes

2 1
()
1 2

No