【VK Cup 2016 - Round 1 (Div 2 Edition)B】【水题】Bear and Displayed Friends 即时维护最大6个数

B. Bear and Displayed Friends

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Limak is a little polar bear. He loves connecting with other bears via social networks. He has n friends and his relation with the i-th of them is described by a unique integer t_i. The bigger this value is, the better the friendship is. No two friends have the same value t_i.

Spring is starting and the Winter sleep is over for bears. Limak has just woken up and logged in. All his friends still sleep and thus none of them is online. Some (maybe all) of them will appear online in the next hours, one at a time.

The system displays friends who are online. On the screen there is space to display at most k friends. If there are more than k friends online then the system displays only k best of them — those with biggest t_i.

Your task is to handle queries of two types:

• "1 id" — Friend id becomes online. It's guaranteed that he wasn't online before.
• "2 id" — Check whether friend id is displayed by the system. Print "YES" or "NO" in a separate line.

Are you able to help Limak and answer all queries of the second type?

Input

The first line contains three integers n, k and q (1 ≤ n, q ≤ 150 000, 1 ≤ k ≤ min(6, n)) — the number of friends, the maximum number of displayed online friends and the number of queries, respectively.

The second line contains n integers t₁, t₂, ..., t_n (1 ≤ t_i ≤ 10⁹) where t_i describes how good is Limak's relation with the i-th friend.

The i-th of the following q lines contains two integers type_i and id_i (1 ≤ type_i ≤ 2, 1 ≤ id_i ≤ n) — the i-th query. If type_i = 1 then a friendid_i becomes online. If type_i = 2 then you should check whether a friend id_i is displayed.

It's guaranteed that no two queries of the first type will have the same id_i becuase one friend can't become online twice. Also, it's guaranteed that at least one query will be of the second type (type_i = 2) so the output won't be empty.

Output

For each query of the second type print one line with the answer — "YES" (without quotes) if the given friend is displayed and "NO" (without quotes) otherwise.

Examples

input

4 2 8
300 950 500 200
1 3
2 4
2 3
1 1
1 2
2 1
2 2
2 3

output

NO
YES
NO
YES
YES

input

6 3 9
50 20 51 17 99 24
1 3
1 4
1 5
1 2
2 4
2 2
1 1
2 4
2 3

output

NO
YES
NO
YES

Note

In the first sample, Limak has 4 friends who all sleep initially. At first, the system displays nobody because nobody is online. There are the following 8 queries:

1. "1 3" — Friend 3 becomes online.
2. "2 4" — We should check if friend 4 is displayed. He isn't even online and thus we print "NO".
3. "2 3" — We should check if friend 3 is displayed. Right now he is the only friend online and the system displays him. We should print "YES".
4. "1 1" — Friend 1 becomes online. The system now displays both friend 1 and friend 3.
5. "1 2" — Friend 2 becomes online. There are 3 friends online now but we were given k = 2 so only two friends can be displayed. Limak has worse relation with friend 1 than with other two online friends (t₁ < t₂, t₃) so friend 1 won't be displayed
6. "2 1" — Print "NO".
7. "2 2" — Print "YES".
8. "2 3" — Print "YES".

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
void fre() { freopen("c://test//input.in", "r", stdin); freopen("c://test//output.out", "w", stdout); }
#define MS(x,y) memset(x,y,sizeof(x))
#define MC(x,y) memcpy(x,y,sizeof(x))
#define MP(x,y) make_pair(x,y)
#define ls o<<1
#define rs o<<1|1
typedef long long LL;
typedef unsigned long long UL;
typedef unsigned int UI;
template <class T1, class T2>inline void gmax(T1 &a, T2 b) { if (b>a)a = b; }
template <class T1, class T2>inline void gmin(T1 &a, T2 b) { if (b<a)a = b; }
const int N = 150010, M = 0, Z = 1e9 + 7, ms63 = 0x3f3f3f3f;
int n, k, q;
int op, o;
int t[N];
set<int>sot;
set<int>::iterator it;
int main()
{
	while (~scanf("%d%d%d", &n, &k, &q))
	{
		sot.clear();
		for (int i = 1; i <= n; ++i)scanf("%d", &t[i]);
		while (q--)
		{
			scanf("%d%d", &op, &o);
			if (op == 1)sot.insert(t[o]);
			else
			{
				bool flag = 0;
				int p = 0;
				if(sot.size())for (it = --sot.end(); ; --it)
				{
					if (++p > k)break;
					if (*it == t[o]) {
						flag = 1; break;
					}
					if (it == sot.begin())break;
				}
				puts(flag ? "YES" : "NO");
			}
		}
	}
	return 0;
}
/*
【题意】
有n（15e4）个朋友
有q（15e4）个事件。
friend list即时只是显示前k（min(6,k)）个在线着
对于每个事件，有两种类型——
（1 id）某人上线
（2 id）询问某人是否在线且排在优先度的前k名

【类型】
水题

【分析】
这题可以直接用set维护。
也可以只维护一个长度为6的数组，记录最大的前6个。

【时间复杂度&&优化】
O(6q)

*/