FAMWEALT - Family members

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Consider a family in the form of a binary tree consisting of male and female nodes. All the left nodes will be male nodes and all the right nodes will be female nodes.

Root node will be female node. The root female initially has a wealth w which she passes on down the tree. The rules are as follows:

  1. all the males in the family pass half of their wealth to each of their children.
  2. all the female nodes pass only half of their wealth to both their children collectively, but the male child suddenly converts it to twice the wealth received.

The members are numbered from 1 to n in the row-wise order. i.e., root will be 1, the two children will be 2 and 3 and so on.

Given wealth W of xth node, you need to find the wealth of yth node.

Input

First line consists of t, the number of test cases (1 ≤ t ≤ 20).

Each of t lines consists of three integer values x, y and W (1 ≤ x, y ≤ 106 and 1 ≤ W ≤ 1000).

Output

For each input test case, print the wealth of yth node in a single line (rounded off to six decimal digits.)

Example

Input:
2
11 3 1
4 6 4

Output:
4.000000
2.000000

hide comments
innovolt: 2014-03-06 23:19:06

weak constraint........AC

vikrant: 2014-03-01 18:29:58

wow ac in first attempt :D

Abhishek Gupta: 2014-02-15 11:04:01

getting wa again & again...any tricky part that one can miss...plz help
i have posted my code at forum>>
[url]
https://www.spoj.com/forum/viewtopic.php?f=3&t=21787&sid=45d4d66470fa23e9ac73ba49ac68702f
[/url]

Last edit: 2014-02-15 11:13:06
aqfaridi: 2014-01-22 15:49:22

@Pandian : You should increase number of test cases to 10^5

BA_AK: 2014-01-21 17:50:18

Too Easy!
Caution: For some algorithms, u need to use long long.

Century on Spoj !! Yeah!

pushkar nagar: 2013-12-31 19:45:45

any tricky test cases....help
wa+wa+wa+wa+wa+wa=i want to do this question anyhow...

Last edit: 2013-12-31 20:18:02
ήάέέϻ Ÿ: 2013-12-30 20:00:35

getting WA again and again.. dnt know wats going wrong :(

Saimadhav Heblikar: 2013-12-27 10:23:40

nice problem.

Chandan Singh: 2013-12-26 10:21:25

Nice problem @Pandian :)

Ankit Kumar: 2013-12-26 10:01:42

Nice problem :)


Added by:Pandian
Date:2013-12-19
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All