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 $M$.

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

```
$L$ $R$
```

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.

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

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:

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