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:
n,m=map(int,raw_input().split())
arr=[0 for x in xrange(m+1)]
for x in xrange(n):
    l,r=map(int,raw_input().split())
    for i in range(l,r+1):
        arr[i]=1
    """if(arr[l]==1):
        if(arr[r]!=1):
            for i in xrange(r,l,-1):
                if(arr[i]==1): break
                arr[i]=1
    elif(arr[r]==1):
        if(arr[l]!=1):
            for i in range(l,r):
                if(arr[i]==1): break
                arr[i]=1
    else:
        for i in range(l,r+1):
            arr[i]=1
    """                    
count=0
ar=list()
#print(arr)
for x in xrange(1,m+1):
    if(arr[x]==0):
        count+=1
        ar.append(str(x))
        
if(count==0):print("0")
else:
    print("%d"%count)
    print(" ".join(ar))