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:
from sys import stdin, stdout
ti = lambda : stdin.readline().strip()
ma = lambda fxn, ti : map(fxn, ti.split())
ol = lambda arr : stdout.write(' '.join(str(i) for i in arr) + '\n')
os = lambda i : stdout.write(str(i) + '\n')
olws = lambda arr : stdout.write(''.join(str(i) for i in arr) + '\n')



n, m = ma(int, ti())
points = [i for i in range(1, m+1)]
ans = [False] * m

for i in range(n):
	l, r = ma(int, ti())
	for j in range(l-1, r):
		ans[j] = True

count = 0 
for i in range(m):
	if not ans[i]:
		count += 1
os(count)

for i in range(m):
	if not ans[i]:
		print i+1,