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:
def sint():
    return (int(input()))

def sints():
    return (map(int, input().split()))

def sara():
    return (list(map(int,input().split())))

def sstr():
    s = input()
    return (list(s[:len(s)]))

def main():
    
    vis = [0]*102
    n, m = sints()
    lst = []
    
    for i in range(n):
        x, y = sints()
        t = (x,y)
        lst.append(t)
        
    lst.sort()
    cnt = 0
    
    for i in lst:
        x, y = i
        if not vis[x]:            
            while not vis[x] and x <= y:
                vis[x] = 1
                x += 1
                cnt += 1
        elif not vis[y]:
            while not vis[y] and y >= x:
                vis[y] = 1
                y -= 1
                cnt += 1
                
    print(m-cnt)
    for i in range(1, m+1):
        if not vis[i]:
            print(i, end = ' ')
    print('')

if __name__ == "__main__":
    main()