CodeForces - 659C Tanya and Toys （map&模拟）

CodeForces - 659C

Tanya and Toys

Time Limit: 1000MS

Memory Limit: 262144KB

64bit IO Format: %I64d & %I64u

Submit Status

Description

In Berland recently a new collection of toys went on sale. This collection consists of 10⁹ types of toys, numbered with integers from 1 to 10⁹. A toy from the new collection of the i-th type costs i bourles.

Tania has managed to collect n different types of toys a₁, a₂, ..., a_n from the new collection. Today is Tanya's birthday, and her mother decided to spend no more than m bourles on the gift to the daughter. Tanya will choose several different types of toys from the new collection as a gift. Of course, she does not want to get a type of toy which she already has.

Tanya wants to have as many distinct types of toys in her collection as possible as the result. The new collection is too diverse, and Tanya is too little, so she asks you to help her in this.

Input

The first line contains two integers n (1 ≤ n ≤ 100 000) and m (1 ≤ m ≤ 10⁹) — the number of types of toys that Tanya already has and the number of bourles that her mom is willing to spend on buying new toys.

The next line contains n distinct integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) — the types of toys that Tanya already has.

Output

In the first line print a single integer k — the number of different types of toys that Tanya should choose so that the number of different types of toys in her collection is maximum possible. Of course, the total cost of the selected toys should not exceedm.

In the second line print k distinct space-separated integers t₁, t₂, ..., t_k (1 ≤ t_i ≤ 10⁹) — the types of toys that Tanya should choose.

If there are multiple answers, you may print any of them. Values of t_i can be printed in any order.

Sample Input

Input

3 7
1 3 4

Output

2
2 5 

Input

4 14
4 6 12 8

Output

4
7 2 3 1

//题意：

有1e9种商品，第i件商品的价格为i元，你已经有了n件商品，现在你有m元，问你还能最多买多少种其他的商品？

//思路：

还是不怎么会用map啊，map太强大了，看了大神的才知道，得活学活用。

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<iostream>
#include<map>
#include<queue>
#define INF 0x3f3f3f3f
#define ull unsigned long long
#define ll long long
#define IN __int64
#define N 100010 
#define M 1000000007
using namespace std;
map<int,bool>mm;
int main()
{
	int t,n,m,i,j,k;	
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		mm.clear();
		while(n--)
		{
			scanf("%d",&k);
			mm[k]=true;
		}
		t=1;
		queue<int>q;
		while(m)
		{
			if(mm[t])
			{
				t++;
				continue;
			}
			if(m-t>=0)
			{
				m-=t;
				q.push(t);
				t++;
			}
			else
				break;
		}
		printf("%d\n",q.size());
		k=0;
		while(!q.empty())
		{
			if(k)
				printf(" ");
			printf("%d",q.front());
			q.pop();k++;
		}
		printf("\n");
	}
	return 0;
}