BALLSUM - Ball sum


You have a bag filled with N balls.Each Ball has a distinct number from 1 to N printed on it.All the numbers are distinct. You withdraw two balls from the bag and take their sum. You need to calculate the probability that the sum is not greater than the given number K(<=N). The Answer should be displayed in the form of p/q.(except when the answer is 0 or 1)

Input

Input consists of various test cases. Each test case consist of two integer inputs,N and K. (0<=K<=N<=1000000000) The program stops taking input when N and K equals -1

Output

Output the result in the form of p/q.(Except when the answer is 0 or 1)

Example

Input:
3 2
100 5
10 6
-1 -1

Output:
0
2/2475
2/15


hide comments
kass_97: 2016-12-30 12:30:37

Took paper and pen, did some thinking and bingo....AC

mrx: 2016-12-11 05:57:12

I don't know why I got TLE. I calculated p and q using maths in O(1) and their gcd using recursion and I used C :/

oh i was declaring long instead of long long :P Sorry !! Easy question !!

Last edit: 2016-12-11 06:57:56
kira28: 2016-12-08 21:04:22

#elementary_school_maths
TOO EASY LOL!!!

rrm_2016: 2016-11-26 21:27:40

Lol...that "/" in "p/q" made me submit one wrong solution...otherwise this is a very eazzyy problem..just high school combinatorics

Last edit: 2016-11-26 21:27:58
hacker_sk: 2016-09-26 11:06:20

as written, it's simple math.. AC in one :)

abhimanyu1996: 2016-08-04 10:53:40

AC in one. #CHAMP

binari: 2016-08-01 22:09:33

Why my code gives wa, I think my code works correct in every status, by the way what should be written when n=0 and k=0 or n=1,k=1 (inputs like this)?

cnexans: 2016-06-19 18:38:55

One of the first problems I solve... O(n) solutions won't work. Although there may be many solutions that can be expressed as a loop, you may find one that has a closed formula :)

vineetpratik: 2016-06-18 17:56:08

o(n) solution won't work
find the general sum equation and calculate the maxima using calculus

Shubham Pandey: 2016-06-06 20:41:55

Author should have framed question properly , problem statement doesn't apply to n<2


Added by:Prateek Agarwal
Date:2015-12-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY