Shirly is a very clever girl. Now she has two containers (A and B), each with some water. Every minute,

she pours half of the water in A into B, and simultaneous pours half of the water in B into A. As the

pouring continues, she finds it is very easy to calculate the amount of water in A and B at any time. It is

really an easy job :).

But now Shirly wants to know how to calculate the amount of water in each container if there are more

than two containers. Then the problem becomes challenging.

Now Shirly has N (2 <= N <= 20) containers (numbered from 1 to N ). Every minute, each container is

supposed to pour water into another K containers ( K may vary for different containers). Then the water

will be evenly divided into K portions and accordingly poured into anther K containers. Now the question

is: how much water exists in each container at some specified time?

For example, container 1 is specified to pour its water into container 1, 2, 3. Then in every minute,

container 1 will pour its 1/3 of its water into container 1, 2, 3 separately (actually, 1/3 is poured back to

itself, this is allowed by the rule of the game).