# #JC0102. Dreamoon and Ranking Collection

ID: 2 Type: RemoteJudge 1000ms 256MiB Tried: 72 Accepted: 32 Difficulty: 4 Uploaded By: Tags>算法基础模拟cf*900

# Dreamoon and Ranking Collection

## Description

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 $v=5$.

## Input

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 $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 100$).

## Output

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.

5
6 2
3 1 1 5 7 10
1 100
100
11 1
1 1 1 1 1 1 1 1 1 1 1
1 1
1
4 57
80 60 40 20

5
101
2
2
60


## Note

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 $1,2,\ldots,101$.