2016年湖南省第十二届大学生计算机程序设计竞赛：G—parathesis

题目链接：传送门

Description

Bobo has a balanced parenthesis sequence P=p 1 p 2…p n of length n and q questions.

The i-th question is whether P remains balanced after p ai and p bi  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').

Input

The input contains at most 30 sets. For each set:

The first line contains two integers n,q (2≤n≤10 5,1≤q≤10 5).

The second line contains n characters p 1 p 2…p n.

The i-th of the last q lines contains 2 integers a i,b i (1≤a i,b i≤n,a i≠b i).

Output

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

Sample Input

4 2
(())
1 3
2 3
2 1
()
1 2

Sample Output

No
Yes
No

解题思路：前缀和+RMQ

用a存储‘（’+1，‘）’-1

若满足匹配，则有任意a[i]>=0

交换两个位置的括弧：‘（’和‘（’，‘）’和‘）’，‘）’和‘（’都不会影响序列的匹配

只有‘（’和‘）’的情况下且a[i]到a[j-1]的最小值小于2才会使序列不匹配

#include   
#include   
#include   
#include   
#include 
#include 
#include 
#include 
#include 
#include