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:
a=input().split()
a[0]= int(a[0])
a[1]= int(a[1])
b = []
for i in range(a[0]):
    b.append(input().split())
    b[i][0]= int(b[i][0])-1
    b[i][1]= int(b[i][1])-1
c = [[n,0] for n in range(a[1])]
for i in range(a[0]):
    if b[i][1]+1>a[1]:
        print(i,c,b,a)
        c[a[1]][1] = 1
    else:
        for l in range(b[i][0],b[i][1]+1):
            c[l][1]=1

temp = []
tempnum = 0
for i in range(a[1]):
    if c[i][1] == 0:
        temp.append((i+1))
        tempnum+=1
if tempnum == 0:
    print(tempnum)
else:
    print(tempnum)
    for i in range(len(temp)):
        print(temp[i], end = ' ')