Problem C
Neural Bakework

Arvid is preparing for the AI Olympiad final. There’s much to do: arranging accommodations, organizing food, preparing problems, and setting up snacks for everyone. Stressed out, Arvid accidentally mixes up the last two tasks. As a participant in the AI Olympiad, you must solve the strange problem that arose.

A neural bakework is a directed graph with $N$ nodes, designed to bake cookies. Initially, $X$ units of ingredients are placed on node $1$, while all other nodes start with zero ingredients. Every second, the following occurs simultaneously for all nodes:

• Let $a_v$ be the number of ingredients on node $v$, and $d_v$ be its out-degree.

• If $d_v = 0$, nothing happens. Otherwise, let $a_v = d_v \cdot q + r$ where $0 \leq r < d_v$. Afterwards send $q$ units of ingredients to each node pointed to by $v$, and keep the remainder $r$.

In other words, each node splits its ingredients as evenly as possible and forwards the result. All updates happen simultaneously across all nodes each second, so the processing order of nodes does not matter.

The ingredients reaching node $N$ become finished cookies. For the neural bakework to be valid, no node may point to itself, and no node may have multiple edges to the same target.

Given integers $X$ and $Y$, your task is to construct a neural bakework that produces exactly $Y$ cookies when $X$ units of ingredients are used. Specifically, the bakework will run for $10^4$ seconds, and if node $N$ ends up with $Y$ cookies, the test case is solved. Your score depends on minimizing $N$.

Input

The input consists of a single line with two integers $X$ and $Y$ ($1 \leq X, Y \leq 10^{18}$).

Output

If no valid neural bakework can produce $Y$ cookies from $X$ ingredients, output $-1$.

Otherwise, output first a line with two integers $N$ and $M$, the number of nodes and edges in your network. Then output $M$ lines, each containing two integers $u_i, v_i$ ($1 \leq u_i, v_i \leq N$), representing an edge from node $u_i$ to $v_i$.

Scoring

There are two test groups that scores indepenedently. Each test group contains a set of test cases.

Let $N_{max}$ be the maximum value of $N$ in your solution across all test cases in a group. If $N_{max} \leq 30$ then you get full points for the group, otherwise, points are calculated as:

where $g$ is the group’s total points ($20$ or $80$).

If $N_{max} \geq 200$ or your answer is incorrect for any test case, you get 0 points for the group.

15 4

8 10
1 2
2 3
3 4
4 2
1 4
1 5
5 6
5 7
6 8
7 8

1 2

-1