Little Scott recently learned how to perform arithmetic operations modulo some
prime number **P**. As a training set he picked two sequences **a** of length
**N** and **b** of length **M**, generated in the following way:

a1=A1  
a2=A2  
ai=(ai-2 * A3 + ai-1*A4 + A5) mod P, for i=3...**N**  
b1=B1  
b2=B2  
bj=(bj-2 * B3 + bj-1 * B4 + B5) mod P, for j=3...**M**  

Now he wants to find the number of pairs (i, j), where 1 ≤ i ≤ **N** and 1 ≤ j
≤ **M**, such that (ai * bj) mod **P** < **L**, for given number **L**. He
asked you to do the same to help him check his answers.

## Input

The first line of input file consists of a single number **T**, the number of
test cases. Each test consists of three lines. The first line of a test case
contains two integers: prime number **P** and positive integer **L**. The
second line consists of six non-negative integers **N**, **A1**, **A2**,
**A3**, **A4**, **A5**. Likewise, the third line contains six non-negative
integers **M**, **B1**, **B2**, **B3**, **B4**, **B5**.

## Output

Output **T** lines, with the answer to each test case on a single line.

## Constraints

**T** = 20  
2 ≤ **P** < 250,000  
**P** is prime   
1 ≤ **L** ≤ **P**  
2 ≤ **N**, **M** ≤ 10,000,000  
0 ≤ **A1**, **A2**, **A3**, **A4**, **A5**, **B1**, **B2**, **B3**, **B4**,
**B5** < **P**