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:
from sys import stdin, stdout 

# string input
n, m = (stdin.readline().split())
 
n, m = int(n), int(m)

arr = []
for x in range(n):
	a, b = stdin.readline().split()
	arr.append((int(a), int(b)))

arr = sorted(arr, key=lambda x: x[0])

x = 1
i = 0
count = 0
ans = []
while(x <= m and i < n):
	if(x >= arr[i][0] and x <= arr[i][1]):
		x+=1
	elif( x > arr[i][1]):
		i+=1
	else:
		count += 1
		ans.append(x)
		x+=1
for x in range(x, m+1):
	count +=1
	ans.append(x)


print(count)
for i in range(len(ans)):
	print(ans[i], end=' ')