Codeforces Round 654 (Div. 2) |
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Finished |
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:
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 $$$10^5$$$.
3 2 3 4 5
1 3
4 3 2 3 5 6
2 3 4
4 3 9 1 1 1
0
In the first test, $$$p=2$$$.
So, the only good number is $$$3$$$.
In the third test, for all positive integers $$$x$$$ the value $$$f(x)$$$ is divisible by $$$p = 3$$$.
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