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
slothsphereoj: 2024-02-29 09:13:03

Test your code here: https://www.udebug.com/SPOJ/BALLSUM

[Sample case]

1000000000 1000000000
3 2
4 4
100 5
10 6
5218372 28732
82671 821
826713 222334
6273 2138
9919921 3231871
1000000000 999772157
-1 -1

[Accepted output]

499999999/999999999
0
1/3
2/2475
2/15
6069635/400461781059
33620/683441157
6178995361/170863389414
95141/1639344
174083061615/3280160757544
62471522744555521/124999999875000000

Simple math with gcd indeed. I can solve BALLSUM but I cannot solve https://www.spoj.com/problems/RABBIT1/.

fuadul_hasan: 2020-06-25 10:42:51

ohh.....! at last i have done it

letuantam96: 2019-03-13 08:54:19

phewwww. finally AC
be careful with extralarge number, u may need long long int type

kushagra_2: 2018-12-14 14:06:04

got it in O(1) :) easy problem needs gcd!!!

anirudnits: 2018-04-25 08:48:01

Got 4 WA's and finally an AC with the same code!!!

flyingduchman_: 2018-04-10 12:35:00

Note that K <= N.

Last edit: 2018-04-22 08:11:52
hello_world123: 2018-03-15 11:08:24

getting tle

srinu_viratian: 2018-01-11 14:55:13

for n=k=0=1
what will be the output?

bayulaxana: 2017-12-29 17:45:39

Very Nice problem...
It consist of mathematics, also GCD.
AC in one go :)

jha4032: 2017-12-27 13:01:56

O(1).............. :)


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