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:
# input n segmentos
# cada segmento tem (1 <= li <= ri <= m)
# considere todos os pontos entre 1 e m inclusive
# print todos os pontos QUE NAO PERTENCEM ao segmento
# o ponto x pertence ao segmento, SE E SOMENTE se l <= x <= r
def transform(x):
    return int(x)

(n, m) = tuple(map(transform,input().split()))
listaDeComparacao = list(range(1,m+1,1))
i = 0
inteiros = {}
numerosForaDoSegmento = []
while(i < n):
    i += 1
    (l,r) = tuple(map(transform,input().split()))
    if(l == r):
        inteiros[l] = l
    for num in list(range(l,r+1,1)):
        inteiros[num] = num

inteiros = sorted(list(inteiros.keys()))

for num in listaDeComparacao:
    if(num not in inteiros):
        numerosForaDoSegmento.append(num)
    
tamanhoLista = len(numerosForaDoSegmento)
if(tamanhoLista != 0):
    print(tamanhoLista)
    print(*numerosForaDoSegmento)
else:
    print(0)