SEQ - Recursive Sequence


Sequence (ai) of natural numbers is defined as follows:

   ai = bi (for i <= k)
   ai = c1ai-1 + c2ai-2 + ... + ckai-k (for i > k)

where bj and cj are given natural numbers for 1<=j<=k. Your task is to compute an for given n and output it modulo 109.

Input

On the first row there is the number C of test cases (equal to about 1000).
Each test contains four lines:

k - number of elements of (c) and (b) (1 <= k <= 10)
b1,...,bk - k natural numbers where 0 <= bj <= 109 separated by spaces
c1,...,ck - k natural numbers where 0 <= cj <= 109 separated by spaces
n - natural number (1 <= n <= 109)

Output

Exactly C lines, one for each test case: an modulo 109

Example

Input:
3 
3 
5 8 2 
32 54 6 
2 
3 
1 2 3 
4 5 6 
6 
3 
24 354 6 
56 57 465 
98765432

Output:
8 
714 
257599514

hide comments
cs215100: 2020-05-20 21:35:01

tle in java. same code ac in c++.

jaybatra: 2020-05-02 18:48:59

can someone explain when I used python 3 it gives TLE but when i used C++ using same logic of matrix exponentiation it passed all the test cases why?

jaybatra: 2020-05-01 10:46:53

I have tried the question using python 3 it is passing the given examples but at the time of submitting it is giving TLE can someone help?

vimi: 2020-04-25 20:36:32

can we apply DP with some memoization? because surely we have overlapping subproblems

jainaagam96: 2020-04-24 20:41:29

i tried threw Python 3 (matrix exponentiation ) But,Giving me TLE

fighter_4: 2020-04-12 07:53:24

accepted,:D

hellb0y_suru: 2020-02-19 15:38:33

Matrix exponentiation !!!
very basic question !!!

lm10_piyush: 2020-02-15 16:37:11

damn hogya!!! if is allowed to provide the solution like here I can post it...

harish_49: 2019-11-03 12:37:34

AC in 0 go !!! Nice problem

devinamuljono: 2019-10-19 09:58:23

manage to get accepted after dealing with some edge case ,


Added by:PaweĊ‚ Dobrzycki
Date:2005-04-29
Time limit:0.5s-3s
Source limit:8196B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:IV Podlasian Contest in Team Programming