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:
config = input()
config_splitted = config.split(" ")
num_segments = int(config_splitted[0])
upper_bound = int(config_splitted[1])
axis = [0] * 110

i = 0
for i in range(num_segments):
    segment = input()
    l = int(segment.split(" ")[0])
    r = int(segment.split(" ")[1])

    j = l
    while (j <= r):
        axis[j] = 1
        j = j + 1

num_not_in_segment = 0
not_in_segment = []

i = 1
while (i <= upper_bound):
    if axis[i] == 0:
        num_not_in_segment = num_not_in_segment + 1
        not_in_segment.append(i)
    i = i + 1
    
print(str(num_not_in_segment))

if num_not_in_segment > 0:
    num = 0
    for num in range(len(not_in_segment)):
        if (num == len(not_in_segment) - 1):
            print(str(not_in_segment[num]))
        else:
            print(str(not_in_segment[num]), end = " ")