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
Deepak Singh Tomar: 2016-03-07 15:56:45

matrix_exponentiation. Thanks fushar :)

minhthai: 2016-02-03 17:26:12

be careful the mod is 10^9 not 10^9 + 7 :)

Ðức Tân: 2015-08-27 18:45:42

dễ vãi

r0bo_dart: 2015-06-25 07:28:24

Hint: While doing matrix multiplication, DON'T do temp[][] += mod(F[][] * M[][]);
instead do temp[][] = mod(temp[][] + F[][] * M[][])
costed me 3 WA's ... phew... best of luck

sHaShAnK sHeKhAr: 2015-06-21 18:23:23

Nice problem to reach 150 :)

i_am_looser: 2015-05-30 15:59:01

learnt something new.......... ; )

sai krishna: 2015-03-11 17:52:35

ha ha ha lot of fun in doing it:)

Ace.JQK: 2014-12-16 11:53:07

multiply matrix

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

I guarantee it will be hell to take the #1 ; but possible.
--edit--> Impossible. Oups.

Last edit: 2014-12-02 01:21:04
Gopal Viswanathan: 2014-12-02 01:44:19

Any Hints?


Added by:Paweł 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