Counting Terms

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When the Chef is not busy with cooking delicious foods, one of his favorite pastime is to solve mathematical problem. But as you know, he is not very good with programming. So when he fails to solve a problem he usually asks John to write a program that will solve it.
Recently the chef became interested in finding the expansion of (x_{1}+x_{2}+....+x_{k})^{n}. Specifically he is more interested in number of terms in it. Being unable to solve the problem he asked John for help. The conversation between John and chef goes as
Chef: Can you write a program that will calculate f(n,k)= number of terms in (x_{1}+x_{2}+....+x_{k})^{n} ?
John: That is a very easy problem.
Chef: Oh, really? Then calculate the sum over (i=0 to n) (f(i,k))
John: That is also an easy problem.
Chef: Then go finish it. And did I mention that I am calculating modulo a prime number p.
John: What?
Chef: Say k=2, n=4, p=3. Then (x_{1}+x_{2})^{4} %3 = (x_{1}^{4}+4 x_{1}^{3} x_{2}+6 x_{1}^{2} x_{2}^{2}+ 4 x_{1} x_{2}^{3} + x_{2}^{4}) %3 = (x_{1}^{4}+ x_{1}^{3} x_{2} + x_{1} x_{2}^{3} + x_{2}^{4}) %3. So if p=3 then f(4,2)=4.
John: OK, I am doing it.
As John started to solve the problem he realized it is not that easy. Now he asked you, his best friend, for help.
As the answer can be quite large print the output modulo 1000003.
Input
Input file starts with a line containing a number T. T lines follow each describing a test case. Each test case consists of a line containing three space separated integers n, k, p.
Output
Output T lines, each line containing the Sum over (i=0 to n) f(i,k) for the given prime p modulo 1000003.
Limit:
1<=T<=10000
0<=n<=10^15
1<=k<=10^15
1<=p<=100
p prime number
Example
Input: 7 10 2 2 10 2 3 10 3 2 10 3 3 4 2 3 3 2 3 0 2 2 Output: 37 42 85 112 12 8 1
Author:  tanaeem 
Tester:  subra 
Editorial  http://discuss.codechef.com/problems/TERM 
Tags  feb11, medium, tanaeem 
Date Added:  3012011 
Time Limit:  1.28 sec 
Source Limit:  50000 Bytes 
Languages:  C, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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