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 PYTHON3):

Solution:
temp = input()
n, m = temp.split(" ")
n, m = int(n), int(m)
segments = []

#print (n, m)

for s in range(n):
  temp = input()
  l0, l1 = temp.split(" ")
  l0, l1 = int(l0), int(l1)
  segments.append([l0,l1])
  
#print(segments)
        
result = []
notinline = 0

for num in range(1, m+1):
  notin = False
  for l in segments:
    #print(num,l[0],l[1])
    if num >= l[0] and num <= l[1]:
      #print("true", num, l[0],l[1])
      notin = False
      break
    else:
      notin = True 
  
  if notin == True:
    notinline += 1
    result.append(num)

print(notinline)
for i in result:
  print(i, end=' ')