Asterism (Easy Version)
Description
This is the easy version of the problem. The difference between versions is the constraints on $n$ and $a_i$. You can make hacks only if all versions of the problem are solved.
First, Aoi came up with the following idea for the competitive programming problem:
Yuzu is a girl who collecting candies. Originally, she has $x$ candies. There are also $n$ enemies numbered with integers from $1$ to $n$. Enemy $i$ has $a_i$ candies.
Yuzu is going to determine a permutation $P$. A permutation is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $\{2,3,1,5,4\}$ is a permutation, but $\{1,2,2\}$ is not a permutation ($2$ appears twice in the array) and $\{1,3,4\}$ is also not a permutation (because $n=3$ but there is the number $4$ in the array).
After that, she will do $n$ duels with the enemies with the following rules:
- If Yuzu has equal or more number of candies than enemy $P_i$, she wins the duel and gets $1$ candy. Otherwise, she loses the duel and gets nothing.
- The candy which Yuzu gets will be used in the next duels.
Yuzu wants to win all duels. How many valid permutations $P$ exist?
This problem was easy and wasn't interesting for Akari, who is a friend of Aoi. And Akari made the following problem from the above idea:
Let's define $f(x)$ as the number of valid permutations for the integer $x$.
You are given $n$, $a$ and a prime number $p \le n$. Let's call a positive integer $x$ good, if the value $f(x)$ is not divisible by $p$. Find all good integers $x$.
Your task is to solve this problem made by Akari.
The first line contains two integers $n$, $p$ $(2 \le p \le n \le 2000)$. It is guaranteed, that the number $p$ is prime (it has exactly two divisors $1$ and $p$).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \le a_i \le 2000)$.
In the first line, print the number of good integers $x$.
In the second line, output all good integers $x$ in the ascending order.
It is guaranteed that the number of good integers $x$ does not exceed $10^5$.
Input
The first line contains two integers $n$, $p$ $(2 \le p \le n \le 2000)$. It is guaranteed, that the number $p$ is prime (it has exactly two divisors $1$ and $p$).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \le a_i \le 2000)$.
Output
In the first line, print the number of good integers $x$.
In the second line, output all good integers $x$ in the ascending order.
It is guaranteed that the number of good integers $x$ does not exceed $10^5$.
Samples
3 2
3 4 5
1
3
4 3
2 3 5 6
2
3 4
4 3
9 1 1 1
0
Note
In the first test, $p=2$.
- If $x \le 2$, there are no valid permutations for Yuzu. So $f(x)=0$ for all $x \le 2$. The number $0$ is divisible by $2$, so all integers $x \leq 2$ are not good.
- If $x = 3$, $\{1,2,3\}$ is the only valid permutation for Yuzu. So $f(3)=1$, so the number $3$ is good.
- If $x = 4$, $\{1,2,3\} , \{1,3,2\} , \{2,1,3\} , \{2,3,1\}$ are all valid permutations for Yuzu. So $f(4)=4$, so the number $4$ is not good.
- If $x \ge 5$, all $6$ permutations are valid for Yuzu. So $f(x)=6$ for all $x \ge 5$, so all integers $x \ge 5$ are not good.
So, the only good number is $3$.
In the third test, for all positive integers $x$ the value $f(x)$ is divisible by $p = 3$.