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.
remaining_segments, deadpoint = input().split()
remaining_segments = int(remaining_segments)
complete_segment = [0]*int(deadpoint)
while remaining_segments > 0:
  remaining_segments -= 1
  start, end = input().split()
  start = int(start)-1
  end = int(end)

  for fill_segment in range(start, end):
    complete_segment[fill_segment] = 1
free_segments = []
number_free_segments = 0
for idx, value in enumerate(complete_segment):
  if value == 0:
    free_segments.append(str(idx+1))
    number_free_segments += 1

if number_free_segments == 0:
  print(0)
else:
  print(number_free_segments)
  print(" ".join(free_segments))

	 			 								 		 			 		  	