ETA

문제

You want to design a level for a computer game. The level can be described as a connected undirected graph with vertices numbered from $11$ to $nn$. In the game, the player's character is dropped at one of the $nn$ vertices uniformly at random and their goal is to reach the exit located at vertex $11$ as quickly as possible. Traversing an edge takes exactly $11$ second.

Figure E.1: Illustration of Sample Output 3, a level where the average optimal time to reach vertex $11$ is $\frac{7}{4}\backslash frac\{7\}\{4\}$.

The difficulty of the level is determined by the average optimal time to reach the exit. Given a target value for this average optimal time, construct a level so that this target value is reached. See Figure E.1 for an example.

입력

The input consists of:

• One line with two coprime integers $aa$ and $bb$ ($1\le a,b\le 10001\; \backslash le\; a,b\; \backslash le\; 1000$) separated by a '/', giving the desired average optimal time to reach the exit as the fraction $\frac{a}{b}\backslash frac\{a\}\{b\}$.

출력

If no connected graph with the average optimal time $\frac{a}{b}\backslash frac\{a\}\{b\}$ to reach vertex $11$ exists, output "impossible". Otherwise, output one such graph in the following format:

• Two integers $nn$ and $mm$ ($1\le n,m\le {10}^{6}1\; \backslash le\; n,\; m\; \backslash le\; 10^6$), the number of vertices and the number of edges.
• $mm$ pairs of integers $uu$ and $vv$ ($1\le u,v\le n1\; \backslash le\; u,v\; \backslash le\; n$), indicating an edge between vertices $uu$ and $vv$.

The graph may include self loops and parallel edges. You are given that if there exists a valid graph, then there also exists one with $1\le n,m\le {10}^{6}1\; \backslash le\; n,\; m\; \backslash le\; 10^6$.

If there are multiple valid solutions, you may output any one of them.