Binomial Coefficient

Problem code: CB01

All submissions for this problem are available.

This is a very simple problem. Given the value of N and K, you need to tell us the value of the binomial coefficient C(N,K). You may rest assured that K <= N and the maximum value of N is 1,000,000,000,000,000. Since the value may be very large, you need to compute the result modulo 1009.

Input

The first line of the input contains the number of test cases T, at most 1000. Each of the next T lines consists of two space separated integers N and K, where 0 <= K <= N and 1 <= N <= 1,000,000,000,000,000.

Output

For each test case, print on a new line, the value of the binomial coefficient C(N,K) modulo 1009.

Example

Input:
3
3 1
5 2
10 3
Output:
3
10
120

Author: moneymachine
Date Added: 16-01-2010
Time Limit: 3 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, FORT, FS, GO, HASK, ICON, JAR, JAVA, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT


Comments

I believe this question has a

amirkg @ 20 Aug 2010 10:40 PM

I believe this question has a wrong test case!

My algorithm is:

I find n!/k! modulo 1009

then i find (n-k)! modulo 1009

and because 1009 is a prime , then both of these numbers are coprime to 1009

and we can use multiplicative inverse of (n-k)! modulo 1009

I tested my program for all inputs less than 1000 with a brute force algorithm. I'm sure my algorithm is right and my program works well. but it says wrong answer!!

Please at least give me the test i'm wrong with.

Thanks

(n-k)! is not coprime to 1009

triplem @ 21 Aug 2010 07:08 AM

(n-k)! is not coprime to 1009 when n-k>=1009, so your algorithm doesn't work.

Thanks

amirkg @ 21 Aug 2010 12:23 PM

Thanks

Then what's your idea?

amirkg @ 21 Aug 2010 12:24 PM

Then what's your idea?

I designed the problem. Use

rahulakaneo @ 21 Aug 2010 06:11 PM

I designed the problem. Use Lucas theorem to solve it.

Sorry for writing in Persian

goharshady @ 22 Aug 2010 02:27 PM

Sorry for writing in Persian but I want to make Amir Understand:

ببین یه قضیه ای وجود داره به نام قضیه ی لوکاس که می گه اگر

p

یک عدد اول باشه اونوقت می شه با یه سری محاسبات راحت باقی مانده ی یک ترکیب بر

p

رو به دست آورد.

ویکیپدیا بخون!

As I saw Mr. Merriman's

goharshady @ 22 Aug 2010 03:00 PM

As I saw Mr. Merriman's answer precomputes C(n,k) for n,k<=1009

I just merged the two algorithms mentioned above. I use Lucas' theorem for big ones and for small ones I find multiplicative inverse of [n-k]! mod 1009.

My solutions are

goharshady @ 7 Sep 2010 09:37 PM

My solutions are memory-friendly :D

Hi guys, This is a problem

p_dawg @ 8 Sep 2012 02:22 PM
Hi guys, This is a problem that I've solved on other language packages, but I am a beginner in C and not so hot in C++. Could you please tell me how to run the files in the examples? What commands are required? I have built the .exe files but I do not see how to use them! Many thanks in advance, p_dawg

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