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:
import re
import math
import decimal
import bisect

def read():
	return input().strip()

def iread():
	return int(input().strip())

def viread():
	return list(map(int, input().strip().split()))

# code goes here
segs = []
n, m = viread()
for i in range(n):
	l, r = viread()
	segs.append((l, False))
	segs.append((r, True))

segs.sort()
# print(segs)
outside = set()
inside = 0
last = 0
for s in segs:
	# print("Checkin'", s[0], "inside", inside, "start of seg", s[1])
	if not inside:
		# print("Update with range", last + 1, "...", s[0], "i.e.", list(range(last + 1, s[0])))
		outside.update(range(last + 1, s[0]))
	elif segs[1]:
		last = s[0]
	inside += 1 if not s[1] else -1
	# print(inside)
outside.update(range(last + 1, m + 1))
print(len(outside))
if len(outside):
	print(*outside)