Problem: 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 ≤ 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.

Input

The first line contains two integers n, p (2 ≤ p ≤ n ≤ 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, …, a_n (1 ≤ a_i ≤ 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.

Examples

Input


3 2
3 4 5


Output


1
3


Input


4 3
2 3 5 6


Output


2
3 4


Input


4 3
9 1 1 1


Output


0

Note

In the first test, p=2.

  * If x ≤ 2, there are no valid permutations for Yuzu. So f(x)=0 for all x ≤ 2. The number 0 is divisible by 2, so all integers x ≤ 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 ≥ 5, all 6 permutations are valid for Yuzu. So f(x)=6 for all x ≥ 5, so all integers x ≥ 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
template <class T1, class T2>
struct cmpf {
  bool rev;
  inline bool operator()(const pair<T1, T2>& a, const pair<T1, T2>& b) const {
    return (a.first < b.first) ^ rev;
  }
  cmpf(bool b = false) { rev = b; }
};
template <class T1, class T2>
struct cmps {
  bool rev;
  inline bool operator()(const pair<T1, T2>& a, const pair<T1, T2>& b) const {
    return (a.second < b.second) ^ rev;
  }
  cmps(bool b = false) { rev = b; }
};
string to_string(const char& c) { return string(1, c); }
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(const bool& b) { return (b ? "true" : "false"); }
string to_string(const vector<bool>& v, const string& sep = " ") {
  string s = "[";
  for (int i = 0; i < v.size(); i++) {
    if (i) {
      s += sep;
    }
    s += to_string(v[i]);
  }
  return s + "]";
}
template <size_t N>
string to_string(const bitset<N>& v) {
  string s = "[";
  for (size_t i = 0; i < N; i++) s += v[i] ? '1' : '0';
  return s + "]";
}
template <class T1, class T2>
string to_string(const pair<T1, T2>& p, const string& sep = ",");
template <class T>
string to_string(const T& v, const string& sep = " ") {
  bool first = true;
  string s = "{";
  for (const auto& x : v) {
    if (!first)
      s += sep;
    else
      first = false;
    s += to_string(x);
  }
  return s + "}";
}
template <class T>
string to_string(const T& v, const int& sz, const string& sep = " ") {
  string s = "[";
  for (int i = 0; i < sz; i++) {
    if (i) {
      s += sep;
    }
    s += to_string(v[i]);
  }
  return s + "]";
}
template <class T1, class T2>
string to_string(const pair<T1, T2>& p, const string& sep) {
  return "(" + to_string(p.first) + sep + to_string(p.second) + ")";
}
long long binpow(const long long& x, const long long& p, const long long& mod) {
  assert(mod > 0);
  if (p == 0) return 1;
  if (p == 1) return x % mod;
  if (p & 1) return (binpow((x * x) % mod, p / 2, mod) * x) % mod;
  return binpow((x * x) % mod, p / 2, mod) % mod;
}
template <class T>
void chmn(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmx(T& a, const T& b) {
  if (a < b) a = b;
}
void setIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
}
int chr[8] = {-1, 0, 1, 0, -1, -1, 1, 1};
int chc[8] = {0, 1, 0, -1, -1, 1, -1, 1};
const long long MOD = 1e9 + 7;
const int INIT = 1001001001;
const int MN = 10001;
long long BIT[MN];
void inc(int pos) {
  for (; pos < MN; pos |= pos + 1) ++BIT[pos];
}
long long query(int pos) {
  long long res = 0;
  for (; pos > 0; pos &= pos - 1) res += BIT[pos - 1];
  return res;
}
long long N, P;
long long A[MN];
long long f(long long x) {
  long long cur = 1;
  for (int i = 0; i < N; i++) {
    long long q = query(x + i + 1);
    if (q <= i) return -1;
    cur = (cur * (q - i)) % P;
  }
  return cur;
}
void solve() {
  cin >> N >> P;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    inc(A[i]);
  }
  vector<int> ans;
  for (int x = 1; x < 4000; x++) {
    if (f(x) > 0) {
      ans.push_back(x);
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) {
    if (i) cout << ' ';
    cout << ans[i];
  }
  cout << endl;
}
int main() {
  setIO();
  long long T = 1;
  while (T-- > 0) solve();
  return 0;
}