A13272. 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 $1,2,\ldots,101$ .