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 PYTHON):

Solution:
class Segment:
	def __init__(self, left, right):
		self.left = left
		self.right = right
	def inSegment(self, x):
		return True if x >= self.left and x <= self.right else False
	def toString(self):
		return " between "+str(self.left)+" and "+str(self.right)

n, m = map(int, raw_input().split(" "))
segments = [ ]
points = [ ]
for i in range(n):
	l, r =  map(int, raw_input().split(" "))
	segments.append(Segment(l, r))
check = [i for i in range(1, m+1)]
for i in range(1, m+1):
	for seg in segments:
		if seg.inSegment(i) and i in check:
			check.remove(i)
print len(check)
s = ""
for k in check:
	s = s + str(k) + " "
print s