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 values x, y and W (1 <= x, y <= 10^6 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
aditya1997: 2016-08-19 17:32:50

nice problem indeed ! XD

pt97: 2016-07-18 21:29:49

xDDD

Siddharth Singh: 2016-06-13 15:08:14

Nice Problem :)

dwij28: 2016-01-20 02:30:43

I was first thinking about finding the lowest common ancestor, but then a better idea came to my mind .. AC in one go .. NIce and simple .. :)

PRINCE KUMAR: 2015-10-01 01:08:56

my 50TH...

Insomniac: 2015-06-27 09:08:23

AC in one go!!.........My 50th :)

:.Mohib.:: 2015-05-23 18:50:05

Awsm que!! Just love to solve this type of que...
Keep sharing que like this... :)

Prakhar Gupta: 2014-08-18 06:08:48

i have a doubt...does the male passes half of its money to both children...that leaves him with zero money, then how come in second test case the male child still have money??

kelaseek: 2014-06-20 12:55:29

float and int is enough for o(logx+logy)

AlcatraZ: 2014-04-23 15:18:20

read question CAREFULLY..costed many WA.. rest is just pen and paper.. Nice problem..


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