POLYMUL  Polynomial Multiplication
Sam and Dean fight the supernatural creatures to protect the humans. Now they have come across a creature called the Vedala, which are always found in pairs. Each Vedala can be represented by a polynomial. Both the Vedalas need to be killed at once or else they can't be killed. They can be killed only by using the product of the two polynomials representing the two Vedala. Help Sam and Dean find the product of the polynomials fast, so they can do their work.
Input
First line contains an integer T (≤ 10), number of test cases.
Each test case will have n (n ≤ 10000), maximum degree of the polynomials on the first line.
Next two lines will have n+1 space separated integers each representing the coefficients of first and second polynomials respectively.
All input coefficients values are <=1000.
Output
For each test case output a line of 2n space separated integers indicating coefficients of the polynomial created after multiplication.
Example
Input: 2 2 1 2 3 3 2 1 2 1 0 1 2 1 0 Output: 3 8 14 8 3 2 1 2 1 0
Explanation
1st test case n=2, the polynomials are x^2 + 2x + 3 and 3x^2 + 2x + 1.
On multiplying we get 3x^4 + 8x^3 + 14x^2 + 8x + 3 and hence the answer is 3 8 14 8 3.
2nd test case n=2, the polynomials are x^2 + 1 and 2x^2 + x.
On multiplying we get 2x^4 + x^3 + 2x^2 + x and hence the answer is 2 1 2 1 0.
hide comments
[Lakshman]:
20210524 10:23:23
Yes, optimized brute force with fast language like c++ has approx the same running time as FFT in a slow language like Java. C++ BF ~ 0.77s while FFT Java ~0.70s Last edit: 20210525 12:12:09 

killer_ash:
20210117 20:24:30
why my n^2 solution get passed? 

akashbhalotia:
20191123 17:46:01
The coefficients will not fit in 32bit integer. 

simantaturja:
20191024 19:09:22
weak dataset 

ankit_mnnit:
20181029 18:55:02
Use long long in place of int for coefficients it causes me 1 WA 

rd10:
20181021 13:42:05
Accepted with plain brute algo with O(n^2) time also. 

mohinem:
20171125 10:50:54
Requires FFT.


weramajstor:
20170812 17:36:02
I'm kind of dissapointed...Before trying to write my first Karatsuba,I tested if this problem would pass with using optimised(fast input) O(n^2) algorithm in C++ and it turns out it does pass...Well atleast you can compare your Karatsuba/FFT time with your O(N^2) algorithm.Constraints should have been 10^5 and then it would be fun Last edit: 20170812 17:37:35 

galloska:
20161101 05:03:28
Just FYI: You have to print 2*n + 1 values. 

Mateus Gonçalves de Oliveira [ITA]:
20151014 04:15:57
Be careful with the limits. The coefficients might not fit in a 32bit integer. 
Added by:  Abhra 
Date:  20140212 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 