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
Pranay Kumar: 2016-01-24 12:09:07

Easy problem if you are into maths! Got AC in 1 go...

try2catch: 2016-01-15 15:53:02

stars and bars

CounterNormalize: 2016-01-14 19:24:10

TLE in python by just using factorial. 2 WA's in C++ due to improper nCr function.
Finally AC though, Really nice implementation!!

Last edit: 2016-01-14 19:24:33
mukesh227194: 2015-11-22 22:13:27

my 100th one!!!!!

irbis9: 2015-11-09 14:47:03

The key is to find the number of ways of selecting k items out of n items such that order doesn't matter and repetition is allowed.

nonushikhar: 2015-10-24 12:00:14

silly mistakes got me 2wa !!!!!! otherwise very easy prob

dragonemperor: 2015-10-19 13:51:38

Bars and stars. AC at first go

farmers_rice: 2015-10-09 02:34:44

keep getting NZEC error even though the only exceptions thrown are in input/output

Sarthak Munshi: 2015-10-06 17:54:01

STARS AND BARS !

xproxmess: 2015-09-27 19:57:49

This is my code - http://ideone.com/UfKbDT
Why is it giving a wrong output for the second test case even though the logic is correct?


Added by:Adrian Kuegel
Date:2004-06-19
Time limit:0.248s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6 VB.net
Resource:own problem