CF1330A Dreamoon and Ranking Collection

Dreamoon is a big fan of the Codeforces contests. One day, he claimed that he will collect all the places from $ 1 $ to $ 54 $ after two more rated contests. It's amazing! Based on this, you come up with the following problem: There is a person who participated in $ n $ Codeforces rounds. His place in the first round is $ a_1 $ , his place in the second round is $ a_2 $ , ..., his place in the $ n $ -th round is $ a_n $ . You are given a positive non-zero integer $ x $ . Please, find the largest $ v $ such that this person can collect all the places from $ 1 $ to $ v $ after $ x $ more rated contests. In other words, you need to find the largest $ v $ , such that it is possible, that after $ x $ more rated contests, for each $ 1 \leq i \leq v $ , there will exist a contest where this person took the $ i $ -th place. For example, if $ n=6 $ , $ x=2 $ and $ a=[3,1,1,5,7,10] $ then answer is $ v=5 $ , because if on the next two contest he will take places $ 2 $ and $ 4 $ , then he will collect all places from $ 1 $ to $ 5 $ , so it is possible to get $ v=5 $ .

The first line contains an integer $ t $ ( $ 1 \leq t \leq 5 $ ) denoting the number of test cases in the input. Each test case contains two lines. The first line contains two integers $ n, x $ ( $ 1 \leq n, x \leq 100 $ ). The second line contains $ n $ positive non-zero integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 100 $ ).

For each test case print one line containing the largest $ v $ , such that it is possible that after $ x $ other contests, for each $ 1 \leq i \leq v $ , there will exist a contest where this person took the $ i $ -th place.

The first test case is described in the statement. In the second test case, the person has one hundred future contests, so he can take place $ 1,2,\ldots,99 $ and place $ 101 $ on them in some order, to collect places $ 1,2,\ldots,101 $ .