Problem Statement

For non-negative integers l and r (l < r), let S(l, r) denote the sequence $(l, l+1, \ldots, r-2, r-1)$ formed by arranging integers from l through r-1 in order. Furthermore, a sequence is called a good sequence if and only if it can be represented as S(2^i j, 2^i (j+1)) using non-negative integers i and j.
You are given non-negative integers L and R (L < R). Divide the sequence S(L, R) into the fewest number of good sequences, and print that number of sequences and the division. More formally, find the minimum positive integer M for which there is a sequence of pairs of $non-negative integers (l_1, r_1), (l_2, r_2), \ldots, (l_M, r_M)$ that satisfies the following, and print such $(l_1, r_1), (l_2, r_2), \ldots, (l_M, r_M)$.

• $L = l_1 < r_1 = l_2 < r_2 = \cdots = l_M < r_M = R$
• $S(l_1, r_1), S(l_2, r_2), \ldots, S(l_M, r_M)$ are good sequences.

It can be shown that there is only one division that minimizes M.

Input

The input is given from Standard Input in the following format:
L R

Output

Print the answer in the following format:
M
l_1 r_1
$\vdots$
l_M r_M

Note that the pairs $(l_1, r_1), \dots, (l_M, r_M)$ should be printed in ascending order.

Constraints

• $0 \leq L < R \leq 2^{60}$
• All input values are integers.

Sample Input 1

3 19

Sample Output 1

5
3 4
4 8
8 16
16 18
18 19

S(3,19)=(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18) can be divided into the following five good sequences, which is the minimum possible number:

• $S(3,4)=S(2^0\cdot 3,2^0\cdot4)=(3)$
• $S(4,8)=S(2^2\cdot 1,2^2\cdot 2)=(4,5,6,7)$
• $S(8,16)=S(2^3\cdot 1,2^3\cdot 2)=(8,9,10,11,12,13,14,15)$
• $S(16,18)=S(2^1\cdot 8,2^1\cdot 9)=(16,17)$
• $S(18,19)=S(2^0\cdot 18,2^0\cdot 19)=(18)$

Sample Input 2

0 1024

Sample Output 2

1
0 1024

Sample Input 3

3940649673945088 11549545024454656

Sample Output 3

8
3940649673945088 3940649673949184
3940649673949184 4503599627370496
4503599627370496 9007199254740992
9007199254740992 11258999068426240
11258999068426240 11540474045136896
11540474045136896 11549270138159104
11549270138159104 11549545016066048
11549545016066048 11549545024454656

见题面 Input 部分

见题面 Output 部分