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  bisect import bisect_right as br
import sys
from collections import *
from math import *
import re
def sieve(n):
    prime=[True for i in range(n+1)]
    p=2
    while p*p<=n:
        if prime[p]==True:
            for i in range(p*p,n+1,p):
                prime[i]=False
        p+=1
    c=0
    for i in range(2,n):
        if prime[i]:
            #print(i)
            c+=1
    return c

def iseven(n):return[False,True][0 if n%2 else 1]
def inp_arr():return list(map(int,input().split()))
def inp():return map(int,input().split())
def lcm(a,b):return (a*b)/gcd(a,b)
max_int = sys.maxsize
mod = 10**9+7

n,m=inp()
arr=[0]*(m+1)
ans,c=[],0
while n:
    a,b=inp()
    for i in range(a,b+1):
        arr[i]+=1
    n-=1
for i in range(1,len(arr)):
    if arr[i]==0:
        c+=1
        ans.append(i)
print(c)
print(*ans)