Problem: You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints. 

Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.

The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.

Output

In the first line print one integer k — the number of points that don't belong to any segment.

In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.

If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.

Examples

Input

3 5
2 2
1 2
5 5


Output

2
3 4 


Input

1 7
1 7


Output

0

Note

In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.

In the second example all the points from 1 to 7 belong to the first segment.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
ostream &operator<<(ostream &os, vector<T> V) {
  for (auto &v : V) os << v << " ";
  return os << "\n";
}
template <class T>
ostream &operator<<(ostream &os, set<T> V) {
  for (auto &v : V) os << v << " ";
  return os << "\n";
}
template <class T, class Y>
ostream &operator<<(ostream &os, map<T, Y> V) {
  for (auto &v : V) os << v << " ";
  return os << "\n";
}
template <class T, class Y>
ostream &operator<<(ostream &os, unordered_map<T, Y> V) {
  for (auto &v : V) os << v << " ";
  return os << "\n";
}
vector<long long> primes = {7, 17, 33, 257, 65537, 1000000007, 1000000009};
int N;
int M;
int a, b;
vector<pair<int, int> > segs;
vector<int> answer;
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(NULL);
  cerr.tie(NULL);
  cin.tie(NULL);
  cin >> N >> M;
  for (auto i = 0; i < N; ++i) {
    cin >> a >> b;
    segs.emplace_back(make_pair(a, 1));
    segs.emplace_back(make_pair(b + 1, -1));
  }
  sort((segs).begin(), (segs).end());
  reverse((segs).begin(), (segs).end());
  int seg_c = 0;
  for (auto i = 1; i < M + 1; ++i) {
    while ((int)((segs).size()) && segs.back().first == i) {
      seg_c += segs.back().second;
      segs.pop_back();
    }
    if (seg_c == 0) answer.emplace_back(i);
  }
  cout << (int)((answer).size()) << "\n";
  for (auto i = 0; i < (int)((answer).size()); ++i) cout << answer[i] << " ";
  cout << "\n";
  return 0;
}