On Thursdays and Fridays, we often say that rounding is approximately equal to having a holiday.

However, Louis is curious whether it is possible to use a rounding method to turn any number into any other number. This way, she could consider any day to be approximately equal to her favorite holiday and be in a good mood every day. To this end, Louis defines an operation that takes the current number $N$, represents it in base $k$ as $N_{(k)}$, and then rounds it at the $i$-th position from the right, denoted as $f(k, i)$. Obviously, for integers, this operation is only meaningful when $1 < i$.

It is worth noting that the rounding in this operation is different from the rounding in everyday life. Formally, for the operation $f(k, p)$, the execution checks the digit $x$ at the $(p-1)$-th position from the right in $N_{(k)}$. When $x \le \lfloor \frac{k}{2} \rfloor$, it will "round down", otherwise it will "round up".

For example, when $N = 20$, the steps to execute the operation $f(8, 2)$ are as follows:

1. Represent $20$ as $24_{(8)}$.
2. Check the digit at the $1$-st position from the right: $4 \le \lfloor \frac{8}{2} \rfloor = 4$.
3. "Round down" the number to $20_{(8)}$, so after the operation $N = 16$.

When $N = 21$, the steps to execute the operation $f(8, 2)$ are as follows:

1. Represent $21$ as $25_{(8)}$.
2. Check the digit at the $1$-st position from the right: $5 > \lfloor \frac{8}{2} \rfloor = 4$.
3. "Round up" the number to $30_{(8)}$, so after the operation $N = 24$.

Now Louis wants to know, for two specific integers $x$ and $y$, a scheme to transform $x$ into $y$ using the provided operations. Since Louis is very eager to have a holiday, the scheme you provide must use no more than $55$ operations.

Input

The input consists of a single line containing two integers $x, y$ ($1 < x, y \le 10^9$).

Output

The first line outputs an integer $n$, representing the number of operations used.

Next, $n$ lines follow, each containing two integers $k_i, p_i$, representing that the $i$-th operation performed is $f(k_i, p_i)$.

For a test case, you are considered to have passed if and only if your output scheme satisfies $0 \le n \le 55$, $1 < k_i \le 10^9$, $1 < p_i \le \lfloor \log_{k_i} 10^9 \rfloor + 1$, and after performing all operations, $x$ becomes $y$, while ensuring that the number never exceeds $2 \times 10^9$ at any time.

Examples

Input 1

6 16

Output 1

2
3 3
16 2

Input 2

7 4

Output 2

1
2 3