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:
str1 = input()
n, m = list(map(lambda x: int(x), str1.split(' ')))
error_set = set()
array = [0]*m


for i in range(n):
    str2 = input();
    l, r = list(map(lambda x: int(x), str2.split(' ')))
    if l == r:
        array[l-1] += 1
        array[r-1] -= 1;
        error_set.add(l-1)
    else:
        array[l-1] += 1
        array[r-1] -= 1;
#print(array)
#print(error_set)
array_num = []
count_num = 0


count = 0
for i in range(m):
    count += array[i]
    if array[i] <0:
        array[i] = count-array[i]
    else:
        array[i] = count
#print(array)

for i in range(m):
    if array[i] == 0 and not(i in error_set):
        array_num.append(i+1)
        count_num += 1

# array = sorted(array)
# for i in range(len(array)):

# print(array)
# count = 0
# count_num = 0
# array_num = []
# j = 0
# q = 0
# for i in range(1, m+1):
#     if j < len(array):
#         if i == array[j][0]:
#             print(i)
#             count += array[j][1];
#             q = array[j][1]
#             j +=1
#     if count == 0 and q !=-1:
#         print('0', i)
#         count_num += 1
#         array_num.append(i)
#     q = 0

print(count_num)
for elem in array_num:
    print(elem, end = ' ')