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
Vipul Pandey: 2014-12-02 01:44:19

nice one to learn a lot of things.

Anirudh: 2014-12-02 01:44:19

Are there any tricky cases in this?

Heisenberg: 2014-12-02 01:44:19

learnt a lot solving this problem :)

যোবায়ের: 2014-12-02 01:44:19

after solving this, try https://www.spoj.pl/problems/SPP/


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