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.
'''
n, m = map(int, input().split())
print(n + m)
'''
'''
n = int(input())
if n == 0:
    print(0)
else:
    a, b = 0, 1
    for i in range(2, n + 1):
        a, b = b, a + b
    print(b)
'''
'''
n, m = map(int, input().split())
print((n ** m) - (m ** n))
'''
'''
n = int(input())
print(n * 2 + 1)
'''
'''
a=int(input())
for i in range(1,a+1):
    if i%2!=0 and a>i:
        print('I hate that',end=' ')
    elif i%2==0 and a>i:
        print('I love that',end=' ')
    elif i%2!=0:
        print('I hate it',end=' ')
    else:
        print('I love it',end=' ')
'''
'''
a = int(input())
l = [[0] * a for i in range(a)]
a1 = []
for i in range(a):
    for j in range(a):
        if i == 0 :
            l[i][j] = 1
        else:
            l[i][j] =l[i - 1][j] + l[i][j -1]
for i in l:
    a1.append(max(i))
print(max(a1))
'''
'''
n = int(input())
cnt = 0
a = []
while n != 0:
	if n % 2 == 1:
		cnt += 1
		a.append(3)
		n -= 3
	else:
		cnt += 1
		a.append(2)
		n -= 2
print(cnt)
for i in a:
	print(i, end = " ")
print()
'''
'''
n = int(input())
t = False
kkk = []
for i in range(0,n):
    p = input().split('|')
    if t == False:
        for j in range(0,2):
            if p[j] == 'OO':
                p[j] = '++'
                t = True
                break
    kkk.append(p[0])
    kkk.append(p[1])
if t == False:
    print('NO')
else:
    print('YES')
    for i in range(0,n):
        print('|'.join(kkk[2*i:2*i+2]))
'''
'''
a=input()
b=list(map(int,input().split()))
c=0
for i in b:
    if b.count(i)>c:
        c=b.count(i)
print(c)
'''
'''
n = int(input())
for i in range(n):
    a, b, k = map(int,input().split())
    zero1 = k // 2
    if k % 2 == 0:
        zero2 = k // 2
    else:
        zero2 = (k // 2) + 1
    b *= zero1
    a *= zero2
    print(a - b)
'''
n, m = map(int, input().split())
a = set(range(1, m + 1))
b = set()
for i in range(n):
	x, y = map(int, input().split())
	for i in range(x, y + 1):
		b.add(i)
for i in b:
	a.discard(i)
print(len(a))
for i in a:
	print(i, end = " ")
print()
