MARBLES - Marbles

Hänschen dreams he is in a shop with an infinite amount of marbles. He is allowed to select n marbles. There are marbles of k different colors. From each color there are also infinitely many marbles. Hänschen wants to have at least one marble of each color, but still there are a lot of possibilities for his selection. In his effort to make a decision he wakes up. Now he asks you how many possibilites for his selection he would have had. Assume that marbles of equal color can't be distinguished, and the order of the marbles is irrelevant.


The first line of input contains a number T <= 100 that indicates the number of test cases to follow. Each test case consists of one line containing n and k, where n is the number of marbles Hänschen selects and k is the number of different colors of the marbles. You can assume that 1<=k<=n<=1000000.


For each test case print the number of possibilities that Hänschen would have had. You can assume that this number fits into a signed 64 bit integer.


10 10
30 7


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tushar8848: 2018-01-08 15:47:56

Admin should revise the test cases. Accepting wrong solutions!!
64 30
correct ans : 759510004936100355
but it is accepting with ans: 310981744965266872
costed me 3WAs

learner4life: 2017-09-16 15:52:57

I appear to have misunderstood the question.

If n = 3, k = 10, the answer should be 0, right ? Because there's no possibility where one marble of each colour is chosen. But the expected answer is 1. Can someone please explain this ?

shubham9261: 2017-09-15 18:05:53

well,,it z smthng like a1+a2+a3+a4+.......+ak=n-k;
just find the total no of permutations for this

vib_s02: 2017-09-06 16:16:38

how do you see those accepted codes?

sid_1462: 2017-06-23 20:20:15

getting TLE in JAVA, not even a single java code accepted in top 70-80

arpit_nitd: 2017-05-27 14:09:13

Beggars Method!!

Last edit: 2017-05-27 14:12:01
sunny: 2017-03-23 13:48:11

bars and stars :-).

rohit9934: 2017-03-17 17:10:37

Solution is hidden in this line "Hänschen wants to have at least one marble of each color". Make a funciton that gives nCr of two numbers and then use your mind.

narutohokage_1: 2017-01-22 06:37:17

Nice question , first did with different approach through recursion took long time to run , i did with first assuming for example if input is 30 7 , then assuming that 7 colors he has chosed now remaining 23 we can put any color in any maner , then did with recursion , then treid to do with combination formula , it was a series , and was too long ,then at last did with the general theme. It is easy , although did not looked at first , answer is right before you.All the best,

davidgalehouse: 2016-09-08 05:44:59

Thought I was doing intermediate calculations the right way but still got integer overflow, so gave up and used BigInteger (not enough test cases to matter much, performance-wise).

Added by:Adrian Kuegel
Time limit:1s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:own problem