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:
n, m = map(int, input().split())

i = 0
starts = []
ends = []
segs = []

while i < n:
    l, r = map(int, input().split())
    starts.append(l)
    ends.append(r)
    segs.append([l, r])
    i += 1

segs.sort(key=lambda seg: seg[0])
ans_points = []
j = 0
i = 1

while i <= m:
    if j >= len(segs):
        ans_points.append(i)
        i += 1
        continue
    if i >= segs[j][0] and i <= segs[j][1]:
        i += 1
        continue
    if i < segs[j][0]:
        ans_points.append(i)
        i += 1
        continue
    if i > segs[j][1]:
        j += 1
        continue

print(ans_points.__len__())

for pt in ans_points:
    print(pt, end=' ')

print()