1023CBracket Subsequence

C. Bracket Subsequence

http://codeforces.com/problemset/problem/1023/C

A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

You are given a regular bracket sequence ss and an integer number kk. Your task is to find a regular bracket sequence of length exactly kk such that it is also a subsequence of ss.

It is guaranteed that such sequence always exists.

Input

The first line contains two integers nn and kk (2≤k≤n≤2⋅1052≤k≤n≤2⋅105, both nn and kk are even) — the length of ss and the length of the sequence you are asked to find.

The second line is a string ss — regular bracket sequence of length nn.

Output

Print a single string — a regular bracket sequence of length exactly kk such that it is also a subsequence of ss.

It is guaranteed that such sequence always exists.

Examples

input

6 4
()(())

output

()()

input

8 8
(()(()))

output

(()(()))

题意：给有n个字符的括号序列（符合规律），输出含k个字符的括号序列（符合规律）。k位偶数

思路：水题。输出第k/2个"("前的序列，然后补齐")"即可。

代码：

#include<iostream>
#include<cstring>
#include<cmath>
#include<iomanip>
#include<algorithm>
#include<cstdio>
#define inf 0x3f3f3f3f
using namespace std;

char s[200005];

int main()
{
    int n,k;
    cin>>n>>k;
    cin>>s;
    int m=k/2;
    int num1=0;
    int sum=0;
    for(int i=0;i<n;i++)
    {
        sum++;
        if(s[i]=='(')
        {
            cout<<"(";
            num1++;
            if(num1==m)
                break;
        }
        else
        {
            cout<<")";
        }
    }
    for(int i=sum+1;i<=k;i++)
        cout<<")";
    cout<<endl;
    return 0;
}