IITKWPCN - Playing With Balls


    There are W white balls and B black balls in a bag. A magician is performing tricks by drawing balls from the bag.

    In each step, the magician randomly removes any two balls from the bag. If the drawn balls are of the same color, he will put one white ball in the bag, otherwise he will put a black ball in it. The two drawn balls from the bag from the ball are discarded.

    He keeps on doing the above tricks until there is only one ball remaining in the bag.

    Given W and B, you have to determine the probability that the color of last ball remaining in the bag is black. You should print the answer with accuracy of upto 6 decimal digits.

Input

    T : no of test cases (1 <= T <= 10^4)

    For every test case W and B  are given (0 <= W <= 10^8 and 0 <= B <= 10^8 and W + B != 0)

Output

    For each test case, output the probability as stated in the problem statement.

Example

Input:
2
1 1
1 2

Output:
1.000000
0.000000

hide comments
pankaj sharma: 2016-06-29 22:11:00

I solved the problem using observation,but I was trying to figure out the general formula for this. Was anyone able to get a general formula of the probability?

hash7: 2016-06-02 20:11:00

dont think as the problem setter wants you to think.. make some sample output and analyze it... you will get a 2 line logic :) nyc question

geoffreymace7: 2015-10-13 08:21:15

Nice question!

dwij28: 2015-09-08 18:46:33

Takes a bit of a time to understand, and then just 3 lines in python. :D

[Mayank Pratap]: 2015-06-09 17:02:37

Solve HC before this ... ..... I solved HC before but had to use arrays ....this time I had no choice.....

ashish jaiswal: 2015-03-27 06:40:05

The two drawn balls from the bag from the ball are discarded..
plz explain me the meaning of ths line??

jobanpreet singh: 2015-02-08 07:16:08

Easy by observation.
But is there any explanaiton which involves concepts of probability??Any link to such an explanation?

Petar Bosnjak: 2014-09-29 23:53:42

so easy :D

siddharth tiwari: 2014-09-29 17:54:16

eurekaaaaaa..!!!

excursionist: 2014-06-29 21:55:02

Easy one :D
got ac


Added by:praveen123
Date:2013-08-06
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:IITK ACA CSE online judge