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;
const long long MAXN = 1123456;
template <typename T>
T sqr(T x) {
  return x * x;
}
template <typename T>
void vout(T s) {
  cout << s << "\n";
  exit(0);
}
long long bp(long long a, long long n) {
  long long res = 1;
  while (n) {
    if (n % 2) res *= a;
    a *= a;
    n >>= 1;
  }
  return res;
}
int main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  long long n, m;
  cin >> n >> m;
  vector<bool> fl(m);
  while (n--) {
    long long l, r;
    cin >> l >> r;
    l--;
    for (int i = l; i < r; i++) fl[i] = 1;
  }
  vector<long long> ans;
  for (int i = 0; i < m; i++)
    if (!fl[i]) ans.push_back(i + 1);
  cout << ans.size() << "\n";
  for (auto i : ans) cout << i << " ";
  return 0;
}