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 PYTHON):

Solution:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

from collections import defaultdict
from math import factorial as f
from fractions import gcd as g

n, m = [int(i) for i in raw_input().split()]
intervals = []
for _ in range(n):
    x, y = [int(i) for i in raw_input().split()]
    intervals.append([x, y])
intervals.sort()
mergedInterval = [intervals[0]]
for interval in intervals:
    if mergedInterval[-1][1] >= interval[0]:
        cur = mergedInterval[-1]
        mergedInterval.pop()
        cur[1] = max(cur[1], interval[1])
        mergedInterval.append(cur)
    else:
        mergedInterval.append(interval)
# print mergedInterval

ret = []
result = mergedInterval[0][0] - 1  # Start from 1..M
for i in range(1, mergedInterval[0][0]): ret.append(i)
for i in range(1, len(mergedInterval)):
    result += mergedInterval[i][0] - mergedInterval[i - 1][1] - 1
    for j in range(mergedInterval[i - 1][1] + 1, mergedInterval[i][0]): ret.append(j)
result += m - mergedInterval[-1][1]
for i in range(mergedInterval[-1][1] + 1, m + 1): ret.append(i)
print result
print " ".join(str(i) for i in ret)