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
shubham9261:
20170915 18:05:53
well,,it z smthng like a1+a2+a3+a4+.......+ak=nk;


vib_s02:
20170906 16:16:38
how do you see those accepted codes?


sid_1462:
20170623 20:20:15
getting TLE in JAVA, not even a single java code accepted in top 7080 

arpit_nitd:
20170527 14:09:13
Beggars Method!! Last edit: 20170527 14:12:01 

sunny:
20170323 13:48:11
bars and stars :).


rohit9934:
20170317 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:
20170122 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:
20160908 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, performancewise). 

sahilagg06:
20160526 20:09:59
Isn't it accepting wrong solution .? 

vijay kumar paliwal:
20160518 12:15:36
Simple..just take care of order of multiplication(start from n) and division(start from 1)...my 50th :) 
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 