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:
from math import *
from collections import *
from itertools import *
from bisect import *
from operator import *
import sys

sys.setrecursionlimit(1000000)


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


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


def o():
    return int(input())


def kl(con, x=0):
    if x == 0:
        print('Yes') if con else print('No')
    elif x == 1:
        print('yes') if con else print('no')
    elif x == 2:
        print('YES') if con else print('NO')
MOD = 1000000007
MAX = 2147483647
MIN = -2147483648
p = input
n,m=io()
l=[]
ans=[]
fg=[0]*101
for _ in range(n):
    a,b=io()
    for i in range(a,b+1):
        fg[i]=1
for i in range(1,m+1):
    if fg[i]==0:
        ans.append(i)
print(len(ans))
print(*ans)