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:
#    !/usr/bin/env python3
#    encoding: UTF-8
#    Modified: <12/Oct/2019 10:59:00 PM>


#    ✪ H4WK3yE乡
#    Mohd. Farhan Tahir
#    Indian Institute Of Information Technology (IIIT), Gwalior


import sys
import os
from io import IOBase, BytesIO


def main():
    n, m=get_ints()
    arr=[0]*(m+1)
    for _ in range(n):
        l, r=get_ints()
        for i in range(l, r+1):
            arr[i]=1
    ans = []
    # op=[]
    # i=1
    # while i<=m:
    #     if arr[i]==0:
    #         for j in range(i, m+1):
    #             if arr[j]==1:
    #                 op.append((i, j-1))
    #                 i=j
    #                 break
    #     else:
    #         i+=1
    # print(len(op))
    # for i in op:
    #     print(*i)

    for i in range(1, m+1):
        if arr[i]==0:
            ans.append(i)
    print(len(ans))
    print(*ans)


BUFSIZE = 8192


class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
         self._file = file
         self._fd = file.fileno()
         self.writable = "x" in file.mode or "w" in file.mode
         self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
         s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
         self.seek((self.tell(), self.seek(0, 2), super(FastIO, self).write(s))[0])
         return s

    def read(self):
         while self._fill():
             pass
         return super(FastIO, self).read()

    def readline(self):
         while self.newlines == 0:
             s = self._fill()
             self.newlines = s.count(b"\n") + (not s)
         self.newlines -= 1
         return super(FastIO, self).readline()

    def flush(self):
         if self.writable:
             os.write(self._fd, self.getvalue())
             self.truncate(0), self.seek(0)


class IOWrapper(IOBase):
     def __init__(self, file):
         py2 = round(0.5)
         self.buffer = FastIO(file)
         self.flush = self.buffer.flush
         self.writable = self.buffer.writable
         if py2 == 1:
             self.write = self.buffer.write
             self.read = self.buffer.read
             self.readline = self.buffer.readline
         else:
             self.write = lambda s: self.buffer.write(s.encode("ascii"))
             self.read = lambda: self.buffer.read().decode("ascii")
             self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)


def get_array(): return list(map(int, sys.stdin.readline().split()))


def get_ints(): return map(int, sys.stdin.readline().split())


def input(): return sys.stdin.readline().strip()


if __name__ == "__main__":
    main()