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:
[segment_number, upper_bound] = [int(x) for x in raw_input().split(" ")]
upper_bound = max(upper_bound, 1)
taken_points = [upper_bound + 1]
for i in range(segment_number):
    [lower_end, upper_end] = [int(y) for y in raw_input().split(" ")]
    for j in range(lower_end, upper_end + 1):
        for k in range(len(taken_points)):
            if taken_points[k] < j:
                continue
            if taken_points[k] > j:
                taken_points.insert(k, j)
            break
taken_points.pop(len(taken_points) - 1)
print(upper_bound - len(taken_points))
i = 1
j = 0
free_points = []
while i != upper_bound + 1:
    if j < len(taken_points):
        if i > taken_points[j]:
            j += 1
            continue
        elif i == taken_points[j]:
            i += 1
            j += 1
            continue
    free_points.append(i)
    i += 1
print(" ".join(str(point) for point in free_points))