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
a_i=(a_i-2 * A3 + a_i-1*A4 + A5) mod P, for i=3...N
b₁=B1
b₂=B2
b_j=(b_j-2 * B3 + b_j-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 (a_i * b_j) 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