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.
list_1  = []
n_m = list(map(int,input().split()))
for i in range(n_m[0]) :
    l_m = list(map(int,input().split()))
    l = l_m[0]
    m = l_m[1]
    if  l == m :
        list_1.append(l)
    if l > m:
        list.append(m)
        while m != l:
            m += 1
            list_1.append(m)

    if l < m:
        list_1.append(l)
        while l != m :
            l += 1
            list_1.append(l)

    l_m.clear()


list_2 = []
a = 1
list_2.append(a)
while a != n_m[1]:
    a += 1
    list_2.append(a)


n = 0
sch = 0
list_3 = []
while n != len(list_2):
    if list_2[n] in list_1:
        sch += 0
    if list_2[n] not in list_1:
        sch += 1
        list_3.append(list_2[n])

    n += 1
print(sch)
for __ in list_3:
    print(__, end = ' ')

