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


hide comments
tarun_28: 2020-04-20 10:01:49

AC with a O(t*(n-1)*(k-1)) DP solution;)

ajaygupta007: 2020-04-07 14:37:34

stars and bar problem

hetp111: 2019-10-14 22:18:25

use r=min(r,n-r) to avoid overflow.

ajaytec227: 2019-09-26 13:05:31

Just find the value it's ok if it overflows.
The right answer for
1000000 500000
is -18446780961959

nitin_uniyal21: 2019-06-21 12:58:37

If you don't know how to proceed. Please see
This will teach you how you can derive the formula (by analyzing the patterns).

toolatetostart: 2019-05-28 11:09:26

find out n-1 C k-1,carefully ,choose iteration as min(n-k,k-1) as nCr can be written as nCn-r

vritta: 2019-05-02 18:24:44

if you are stuck then this - might help (contains explanation along with code).
Also please don't post unproductive comments like "A.C. in one go" etc. Nobody cares about your A.C.

harry_shit: 2019-01-14 09:42:28

i am in love with spoj!!

suraj_13: 2019-01-10 20:12:15

calculate C(n-1, k-1)
the problem is just the another variant of stars and bars.
the proof is left as an exercise.

Muhammad Ashlah Shinfain: 2018-04-01 09:29:00

i think if this solution is not intended using big integer the answer in description should be mentioned to modulo with a value (such as 1000000007)

I found C(999999,499999), which I think would be possibly computed in one of the testcase, is very big. It is aprox. 300000 digits,499999)

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