POWPOW - Power with Combinatorics

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Your task is to find a^(exp^(b)),

a: Provided in input,10^5 => a >= 0

b: Provided in Input,10^5 => b >= 0

exp=(nC0)^2 + (nC1)^2 +(nC2)^2+ ... +(nCn)^2,

n: Provided in the input, 10^5 => n >= 0

As the answer can be too large , you need to output modulo 10^9+7.

nCr denotes n choose r.


The first line of each input file contains number of test cases t (t<=1000).

Then follow a new line.

Then follow t lines, each containing 3 integers, (i.e. a b n  in order) each of them separated by a space.


Output Contains t lines, ith line contains the answer of the ith test case .


1 1 1



In First test case, the Value of exp is 2, value of 1^(2^1) is 1, so output is 1.

Click here to see my set of problems at Spoj.

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origin_beta: 2023-03-20 17:39:41

- would start with little fermat and derive exp^b in terms of mod p-1
- afterwards, use vandermon to derive simplification of exp
- then, use chinese remainder thereom to find C(2n, n)
- rest is straightforward

sankalp_7: 2021-07-09 19:41:28

What is there in test case 8 :(
Got so many WAs without even a hint.
Please help...
Finally removed from todo list after 10 months...
No words to describe the beauty of the problem...

Last edit: 2022-05-07 11:24:52
abhinav_jain02: 2019-06-15 09:08:12

Pre requisites:
1. Fermat's little theorem
2. Lucas theorem
3. Chinese remainder theorem
4. Modular exponentiation
5. Modular multiplicative inverse
6.Extended Euclidean Theorem

For those getting WA on test case 8:
Try to check your computation for exp

For those getting TLE on test case 8:
Try to do some pre computation

Excellent problem to get strengthen all your mathematical concepts in competitive coding .
AC after 8 attempts after getting WA and TLE on test case 8

Last edit: 2019-06-15 09:10:57
kmkhan_014: 2018-05-09 06:01:44

Anyone please comment the result for:
2 2 2

yash_code_guy: 2017-01-10 03:39:44

Wow What a question
My 50th :)

Last edit: 2017-01-21 14:41:57
Tanzir Islam: 2015-07-20 15:53:13

I got ac in this problem. However, there's something weird about this problem.
In my solution, I wrote the function to calculate power like this,
long long power(long long a, long long b, long long p)
if(a == 0)
return 0;
I got wa. Then I removed this if condition, I got ac. 0^b should be 0 for any value of b, shouldn't it ?

Sayak Haldar: 2015-01-25 14:59:55

@psetter, is 0^0=1? like in powpow2 and tutorial version of it?
edit 1: anyone who solves this problem, please help me by giving the answer..

Last edit: 2015-01-25 15:39:21
i need you: 2014-12-10 16:44:28

getting wrong answer in 8th judge...please suggest

Last edit: 2015-02-02 11:29:09
Mayank Ladia: 2014-11-30 17:34:32

testcase 8.. WA now :(

Last edit: 2015-07-13 23:02:16
tapan sahni: 2014-07-28 15:37:21

getting nzec in java ...what to do

Added by:devu
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64