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:
def cacute(m, n, values=None):
    not_belong = []
    if  m > 100 or m < 0:
        print len(not_belong)
    if n < 0:
        print len(not_belong)
    if not values:
        print len(not_belong)
    if len(values) != n:
        print len(not_belong)
    for i in xrange(1, m + 1, 1):
        in_ = False
        for li, lr in values:
            if li <= i and i <= lr:
                in_ = True
                break
        if not in_:
            not_belong.append(i)
    print len(not_belong)
    if not_belong:
        print ' '.join([str(i) for i in not_belong])

n, m = raw_input().split(' ')
values = []

for i in range(int(n)):
    a = raw_input()
    if a != '':
        k, v = a.split(' ')
        values.append((int(k), int(v)))

cacute(int(m), int(n), values)