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.
Input
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.
Output
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.
Example
Input: 2 10 10 30 7 Output: 1 475020
hide comments
nodiveg:
20241019 18:11:06
Can anyone explain why my idea is wrong for tc 2 where I chose all 7 marbles among 30 of different kinds and now I have left 23 marbles as I already chose at least one of each kind by choosing 7 marbles among 30 now for each marble I have 7 possibilities so why the answer is not 7^23 ?? can anyone explain


eyad9090:
20231113 09:56:44
if you coudn't understand how to get this formula watch this two videos


tarun_28:
20200420 10:01:49
AC with a O(t*(n1)*(k1)) DP solution;) 

ajaygupta007:
20200407 14:37:34
stars and bar problem 

hetp111:
20191014 22:18:25
use r=min(r,nr) to avoid overflow. 

ajaytec227:
20190926 13:05:31
Just find the value it's ok if it overflows.


nitin_uniyal21:
20190621 12:58:37
If you don't know how to proceed. Please see https://www.youtube.com/watch?v=UTCScjoPymA


toolatetostart:
20190528 11:09:26
find out n1 C k1,carefully ,choose iteration as min(nk,k1) as nCr can be written as nCnr 

vritta:
20190502 18:24:44
if you are stuck then this  <snip> might help (contains explanation along with code).


harry_shit:
20190114 09:42:28
i am in love with spoj!! 
Added by:  Adrian Kuegel 
Date:  20040619 
Time limit:  1s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  own problem 