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=input()
decomp=n_m.split(" ")
n=int(decomp[0])
m=int(decomp[1])
c=n
res=""
otrezok_max=list(range(1, m+1))
otrezki=[]
tochki1=[]
tochki=[]
while n!=0:
    otrezok=input()
    decomp=otrezok.split(" ")
    otrezki.append(decomp)
    n-=1
for i in range(0, c):
    a=int(otrezki[i][0])
    b=int(otrezki[i][1])
    num=list(range(a, b+1))
    tochki1.append(num)
for i in range(0, len(tochki1)):
    for j in range(0, len(tochki1[i])):
        tochki.append(tochki1[i][j])
tochki=set(tochki)
tochki=list(tochki)
for i in range(0, len(tochki)):
    otrezok_max.remove(tochki[i])
for i in range(0, len(otrezok_max)):
    q=otrezok_max[i]
    res+=str(q)+" "
print(len(otrezok_max))
print(res)