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;
int main() {
  int n = 0, m = 0;
  cin >> n >> m;
  vector<int> vec(n * 2, 0);
  for (int i = 0; i < n * 2; i++) cin >> vec[i];
  vector<bool> fr(m + 1, 0);
  for (auto i : vec) fr[i] = 1;
  int counter = 0;
  for (int i = 0; i < vec.size() - 1; i += 2) {
    for (int j = vec[i]; j <= vec[i + 1]; j++) {
      fr[j] = 1;
    }
  }
  for (int i = 1; i < fr.size(); i++)
    if (fr[i] == 0) counter++;
  cout << counter << endl;
  for (int i = 1; i < fr.size(); i++)
    if (fr[i] == 0) cout << i << " ";
  cout << endl;
  return 0;
}