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
Vipul Pandey: 2014-01-05 21:57:12

easy if you get it. Otherwise a good problem of probability.

tbos: 2014-01-04 15:03:13

AC in a Go
:):D \o/

Last edit: 2014-01-04 15:19:47
ritz: 2014-01-04 14:04:40

nice problem statement :) (Y)

ABHISHEK004: 2014-01-02 20:51:00

simple....
similar to HAPPY COINS.... :)

RG: 2013-12-30 06:58:54

Yeah its really too simple... No need for programming Simple probability.. :)

Ankit Kumar: 2013-12-24 12:38:35

Hint : It's just TOO simple ;)
and a beautiful question too!!!

Last edit: 2013-12-24 12:38:57
Anubhav Balodhi : 2013-12-23 19:48:03

Good Q on Probability theory...

Raman Shukla: 2013-08-24 12:38:24

Nice one... My 150th Classical on spoj...


Added by:praveen123
Date:2013-08-06
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:IITK ACA CSE online judge