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Олимпиадные задачи на английском языке

21/02/2009 | Занятие 13 (E) |

*Ограничения: время – 2s/4s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод*

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By the year 3141, the human civilization has spread all over the galaxy.
The special hypertunnels are used to travel from one star system to another.
To use the hypertunnel, you fly to a special location near the source
star using your spaceship, activate the hyperjumper, fly through the
hypertunnel, get out near your destination star and fly to the planet
you need. The whole process takes exactly one day. A small drawback
of the system is that for each tunnel every day only one spaceship
can travel using this tunnel.

You are working in the transportation department
of the "Intergalaxy Business Machines" company.
This morning your boss has assigned a new task to you.
To run the programming contest IBM needs to deliver `K` supercomputers
from Earth where the company headquarters are located to the
planet Eisiem. Since supercomputers are very large, one needs
the whole spaceship to carry each supercomputer. You are asked to
find a plan to deliver the supercomputers that takes as few days as
possible. Since IBM is a very powerful corporation, you may assume
that any time you need some tunnel for hyperjump, it is at your service.
However, you still can use each tunnel only once a day.

Input consists of several datasets. The first line of each dataset
contains `N` – the number of star systems in the galaxy, `M` – the number
of tunnels, `K` – the number of supercomputers to be delivered, `S` – the
number of the solar system (the system where planet Earth is) and `T` – the
number of the star system where planet Eisiem is (`2\ ≤\ N\ ≤\ 50`,
`1\ ≤\ M\ ≤\ 200`, `1\ ≤\ K\ ≤\ 50`, `1\ ≤\ S,\ T\ ≤\ N`, `S\ ≠\ T`).

Next `M` lines contain two different integer numbers each and describe
tunnels. For each tunnel the numbers of star systems
that it connects are given. The tunnel can be traveled in
both directions, but remember that each day only one ship can
travel through it, in particular, two ships cannot simultaneously
travel through the same tunnel in opposite directions.
No tunnel connects a star to itself and any two stars are
connected by at most one tunnel.

On the first line of the output for each dataset print `L` – the fewest
number of days needed to deliver `K` supercomputers from star system `S` to
star system `T` using hypertunnels. Next `L` lines must describe
the process. Each line must start with `C_i` – the number of ships
that travel from one system to another this day. `C_i` pairs of
integer numbers must follow, pair `A\ \ B` means that the ship number `A`
travels from its current star system to star system `B`.

It is guaranteed that there is a way to travel from star system `S`
to star system `T`.

Sample Input

6 7 4 1 6 1 2 2 3 3 5 5 6 1 4 4 6 4 3

Sample Output

4 2 1 2 2 4 3 1 3 2 6 3 4 3 1 5 3 6 4 4 2 1 6 4 6