SEQ  Recursive Sequence
Sequence (a_{i}) of natural numbers is defined as follows:
a_{i} = b_{i} (for i <= k)
a_{i} = c_{1}a_{i1} + c_{2}a_{i2} + ... + c_{k}a_{ik} (for i > k)
where b_{j} and c_{j} are given natural numbers for 1<=j<=k. Your task is to compute a_{n} for given n and output it modulo 10^{9}.
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)
b_{1},...,b_{k}  k natural numbers where 0 <= b_{j} <= 10^{9} separated by spaces
c_{1},...,c_{k}  k natural numbers where 0 <= c_{j} <= 10^{9} separated by spaces
n  natural number (1 <= n <= 10^{9})
Output
Exactly C lines, one for each test case: a_{n} modulo 10^{9}
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
maratha:
20190726 19:14:21
You might find problem 'Retrospective Sequences' on codeforces gym similar to this.(Slight variation) Last edit: 20190726 19:15:33 

sagar_june97p:
20190612 14:07:21
AC in One go!!! 

surajk543:
20181019 14:05:29
Got Accepted Finally...YAAHOOOO>>> 

masterchef2209:
20180907 23:30:45
AC in 1 go


riyuzaki251097:
20180814 23:10:21
though concept is easier to think but implementation took me hours


hrsh_sengar:
20180314 09:06:48
My 100th :)


aruneshg:
20171226 16:41:57
when to take mod


amulyagaur:
20170830 20:26:50
ac in 1 go 

babur:
20170822 19:43:16
How can output of 3rd case be 257599514, this number is greater than 1e9 and so by modulo the output must be 57599514. Where am I going please help.. 

Rajat Sharma:
20160806 13:56:12
Java: will learn matrix exponentiation with recursion, linear recursive equations, how to solve these equations by converting the addition into multiplicative expressions i.e. through matrices.

Added by:  PaweÅ‚ Dobrzycki 
Date:  20050429 
Time limit:  0.5s3s 
Source limit:  8196B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  IV Podlasian Contest in Team Programming 