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:
import sys
r = lambda: sys.stdin.readline()
n, m = map(int,r().split())
d=[]
d2=[]
ddd=[]
for a in range(1,m+1):
    d=d+[a]

for a in range(n):
    i, j = map(int,r().split())
    for b in range(i, j+1):
        d2=d2+[b]
d2=list(set(d2))

for a in range(len(d)):
    cc=0
    for b in range(len(d2)):
        if d[a]==d2[b]:
            cc=1
    if cc ==0:
        ddd = ddd + [d[a]]

print(len(ddd))
c2=""
for a in range(len(ddd)):
    if a== len(ddd):
        sys.stdout.write(str(ddd[a]))
    else:       
        sys.stdout.write(str(ddd[a])+" ")