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() {
  long long int n, m;
  cin >> n >> m;
  int x, y;
  vector<pair<int, int> > A(n);
  vector<int> B;
  for (int i = 0; i < n; i++) {
    cin >> x >> y;
    A[i].first = x;
    A[i].second = y;
  }
  sort(A.begin(), A.end());
  int last = 0, next;
  for (int i = 0; i < A.size(); i++) {
    next = A[i].first;
    if (next < last) {
      if (A[i].second > last) last = A[i].second;
      continue;
    }
    last++;
    while (last < next) {
      B.push_back(last);
      last++;
    }
    last = A[i].second;
  }
  last++;
  while (last < m + 1) {
    B.push_back(last);
    last++;
  }
  int size = B.size();
  cout << size << endl;
  for (int i = 0; i < size; i++) {
    cout << B[i] << " ";
  }
  return 0;
}