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>
int arraynobelong[100];
int main() {
  int segments, upperbound, repeat1, repeat2, check = 0, counter = 0,
                                              pointsnobelong = 0;
  scanf("%d %d", &segments, &upperbound);
  int arrays[2 * segments];
  for (repeat1 = 0; repeat1 < 2 * segments; repeat1 += 2) {
    scanf("%d %d", &arrays[repeat1], &arrays[repeat1 + 1]);
  }
  for (repeat1 = 1; repeat1 <= upperbound; repeat1++) {
    for (repeat2 = 1; repeat2 < 2 * segments; repeat2 += 2) {
      if (repeat1 >= arrays[repeat2 - 1] && repeat1 <= arrays[repeat2]) {
        counter++;
      }
    }
    if (counter == 0) {
      arraynobelong[check] = repeat1;
      check++;
      pointsnobelong++;
    }
    counter = 0;
  }
  if (pointsnobelong != 0) {
    printf("%d\n", pointsnobelong);
    for (repeat1 = 0; repeat1 < pointsnobelong; repeat1++) {
      printf("%d ", arraynobelong[repeat1]);
    }
  } else {
    printf("%d", 0);
  }
  return 0;
}