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:
n,m = [int(i) for i in input().split()]


ls = [[0] for i in range(0,m+1)]

for i in range(n):
    j,k = [int(i) for i in input().split()]

    for l in range(j,k+1):
        ls[l][0]=1


count = 0
res = []
for j in range(1,len(ls)):
    if ls[j][0]==0:
        count +=1
        res.append(j)
print(count)
if count:
    print(*res,end=" ")

# 100 100
# 51 82
# 14 81
# 17 37
# 78 92
# 15 64
# 8 86
# 8 89
# 77 87
# 10 66
# 12 15
# 25 100
# 47 92
# 21 78
# 20 63
# 13 49
# 36 41
# 41 79
# 16 87
# 69 87
# 3 76
# 60 80
# 49 100
# 59 70
# 8 72
# 38 71
# 45 97
# 14 71
# 54 76
# 4 81
# 46 59
# 29 39
# 3 92
# 22 49
# 53 99
# 52 59
# 31 74
# 43 92
# 23 42
# 9 44
# 47 82
# 7 40
# 9 12
# 3 55
# 37 85
# 22 46
# 52 84
# 41 98
# 21 77
# 17 63
# 62 91
# 43 64
# 13 30
# 19 58
# 33 57
# 8 14
# 65 85
# 5 68
# 1 44
# 51 85
# 7 68
# 47 100
# 9 49
# 78 79
# 39 87
# 67 77
# 62 69
# 24 55
# 42 87
# 37 73
# 81 85
# 26 60
# 5 38
# 40 84
# 42 4