## 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
```

 < Previous 1 2 3 Next > 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/