research-on-numbers-1
Source: hackerearth
Difficulty: HARD

Bob is studying in a research institute. He is currently researching on integer sequences. He has already done some research on famous fibonacci sequence. Now he is trying to investigate patterns in a general recursive sequence (Ai) 
Sequence  (Ai) is 
Ai =  Bi (for i ≤ k) 
Ai = C1 * Ai-1 + C2 * Ai-2 +.......+ Ck*Ai-k (for i > k) 

But while calculating the sequence he realizes that values are growing very fast. So to keep the values small he calculates values modulo 10^9+7 (1000000007) . So that each term of sequence will be less than 10^9+7.

While he is busy with his work, his girlfriend is disturbing him a lot. He wants to make her busy with some task. He gives her the task of sorting all the terms from Al to Ar of his sequence. She is very quick so he gives her same task Q times (of course with different l and r). Since sorting is very boring task so she asks you to complete the task. 
You will be given two numbers l and r and you are expected to output all the terms from Al  to Ar  in non decreasing order. But to avoid such a large output, if there are more than 100 terms in the output print only first 100.

Input :
First line contains T, the number of test cases. First line of each test case contains two space separated integers Q and k. Next line contains array B of length k. 3^rd line contains array C of length k. Each of next Q lines contains two space separated integers l and r.

Output : 
For each test case output Q lines. Each line contains terms from Al to Ar in non decreasing order. If more than 100 terms are there to output,print only first 100 
Constraints : 
1 ≤ T ≤ 3 
1 ≤ Q ≤ 100  
1 ≤ k ≤ 5  
1 ≤ Bj,Cj ≤ 50  
1 ≤ l,r ≤ 10^6  
l ≤ r 

SAMPLE INPUT
2
4 3
1 2 3
2 1 1
1 5
6 8
8 9
6 9
3 4
4 5 7 9
2 2 1 3
2 7
10 12
100 101

SAMPLE OUTPUT
1 2 3 9 23
58 148 377
377 960
58 148 377 960
5 7 9 49 138 404
9964 29126 85073
483689722 905484679