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.
def pointsInSegments(coordinates, m):
    coordinates.sort(key=lambda tup: tup[0])
    curr_segment = 0
    not_belonging = ""
    for curr_num in range(1, m+1):
        while curr_segment < len(coordinates):
            if coordinates[curr_segment][0] > curr_num:
                not_belonging += str(curr_num) + " "
                break
            if (coordinates[curr_segment][0] <= curr_num and coordinates[curr_segment][1] >= curr_num):
                break
            curr_segment+=1
        if curr_segment >= len(coordinates):
            not_belonging += str(curr_num) + " "
    if not_belonging == "":
        return "0\n"
    else:
        return str(len(not_belonging.split()))+"\n"+not_belonging

data = input().split()
n = int(data[0])
m = int(data[1])
segments = []
for i in range(n):
    segment = input().split()
    segments.append((int(segment[0]), int(segment[1])))

print(pointsInSegments(segments, m))