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.
#import resource
#import sys
#resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])
#import threading
#threading.stack_size(2**26)
#sys.setrecursionlimit(0x1000000)
from sys import stdin, stdout
mod=(10**9)+7
mod1=mod-1
def modinv(n,p):
    return pow(n,p-2,p)
fact=[1]
for i in range(1,100001):
    fact.append((fact[-1]*i)%mod)
def ncr(n,r,p):
    t=((fact[n])*(modinv(fact[r],p)%p)*(modinv(fact[n-r],p)%p))%p
    return t
def GCD(x, y):
   while(y):
       x, y = y, x % y
   return x
def BS(arr, l, r, x):
    if r >= l:
        mid = l + (r - l)/2
        if arr[mid] == x:
            return mid
        elif arr[mid] > x:
            return BS(arr, l, mid-1, x)
        else:
            return BS(arr, mid+1, r, x)
    else:n -1
from bisect import bisect_left as bl
from bisect import bisect_right as br
import itertools
import math
import heapq
from random import randint as rn
from Queue import Queue as Q
def comp(x,y):
    if(x[0]<y[0]):
        return -1
    elif(x[0]==y[0]):
        if(x[1]<y[1]):
            return -1
        else:
            return 1
    else:
        return 1
def find(x):
    if(p[x]!=x):
        p[x]=find(p[x])
    return p[x]
def union(x,y):
    m=find(x)
    n=find(y)
    if(m!=n):
        s[0]-=1
        if(r[m]>r[n]):
            p[n]=m
        elif(r[n]>r[m]):
            p[m]=n
        else:
            p[n]=m
            r[m]+=1
"""*********************************************************************************"""
n,m=map(int,raw_input().split())
b=[0]*(m+1)
for i in range(n):
    x,y=map(int,raw_input().split())
    for j in range(x,y+1):
        b[j]=1
s=[]
t=0
for i in range(1,m+1):
    if(b[i]==0):
        s.append(str(i))
        t+=1
print t
print " ".join(s)
