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 functools import cmp_to_key
class seg():
    def __init__(self, x, y):
        self.l = x
        self.r = y

    def __str__(self):
        return '[{}, {}]'.format(self.l, self.r)

def mycomp(a, b):
    if a.l > b.l:
        return 1
    elif a.l == b.l:
        return 0
    else:
        return -1
mycomp = cmp_to_key(mycomp)

def merge(arr, n):
    # print(arr)
    arr.sort(key=mycomp, reverse = True)
    # print(arr)
    index = 0
    for i in range(n):
        if index != 0 and arr[index-1].l <= arr[i].r:
            while index != 0 and arr[index-1].l <= arr[i].r:
                arr[index-1].r = max(arr[index-1].r, arr[i].r)
                arr[index-1].l = min(arr[index-1].l, arr[i].l)
                index -= 1
        else:
            arr[index] = arr[i]
        index += 1
    ans = []
    for i in range(index):
        ans.append(arr[i])
    return ans

if __name__ == '__main__':
    n, m = tuple(map(int, input().split()))
    arr = []
    for i in range(n):
        x, y = tuple(map(int, input().split()))
        arr.append(seg(x,y))
    ans = merge(arr, n)
    cnt = 0
    res = []
    flg = False
    for i in range(1, m+1):
        for z in ans:
            flg |= (i in range(z.l, z.r+1))
        if not flg:
            cnt += 1
            res.append(i)
        flg = False
    print(cnt)
    if len(res) > 0:
        for k in res:
            print(k, end=' ')
        print()