Tanya and Toys

题意翻译

输入 $n,m,n$ 表示你有的玩具个数，$m$ 表示你有的钱，下一行输入 $n$ 个数，表示你已拥有的玩具编号。 你想买玩具，但不想买重复的。求你最多还可以买多少个玩具，并输出买这么多个玩具时其中任意一种你买的所有玩具的编号 玩具的价格等于其编号。

题目描述

In Berland recently a new collection of toys went on sale. This collection consists of $ 10^{9} $ types of toys, numbered with integers from $ 1 $ to $ 10^{9} $ . A toy from the new collection of the $ i $ -th type costs $ i $ bourles. Tania has managed to collect $ n $ different types of toys $ a_{1},a_{2},...,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.

输入输出格式

输入格式

The first line contains two integers $ n $ ( $ 1<=n<=100000 $ ) and $ m $ ( $ 1<=m<=10^{9} $ ) — 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 $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{9} $ ) — the types of toys that Tanya already has.

输出格式

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 exceed $ m $ . In the second line print $ k $ distinct space-separated integers $ t_{1},t_{2},...,t_{k} $ ( $ 1<=t_{i}<=10^{9} $ ) — 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.

输入输出样例

输入样例 #1

3 7
1 3 4

输出样例 #1

2
2 5 

输入样例 #2

4 14
4 6 12 8

输出样例 #2

4
7 2 3 1

说明

In the first sample mom should buy two toys: one toy of the $ 2 $ -nd type and one toy of the $ 5 $ -th type. At any other purchase for $ 7 $ bourles (assuming that the toys of types $ 1 $ , $ 3 $ and $ 4 $ have already been bought), it is impossible to buy two and more toys.