A polynomial in x of degree D can be written as:

a_Dx^D + a_D-1x^D-1 + ... + a₁x¹ + a₀

In some cases, a polynomial of degree D can also be written as the product of two polynomials of degrees D₁ and D₂, where D = D₁ + D₂. For instance,

4 x² + 11 x ¹ + 6 = (4 x¹ + 3) * (1 x¹ + 2)

In this problem, you will be given two polynomials, denoted F and G. Your task is to find a polynomial H such that G * H = F, and each a_i is an integer.

Input

You should first read an integer N ≤ 60, the number of test cases. Each test case will start by describing F and then describe G. Each polynomial will start with its degree 0 ≤ D ≤ 20, which will be followed by D+1 integers, denoting a₀, a₁, ... , a_D, where -10000 ≤ a_i ≤ 10000. Each polynomial will have a non-zero coefficient for it's highest order term.

Output

For each test case, output a single line describing H. If H has degree D_H, you should output a line containing D_H + 1 integers, starting with a₀ for H. If no H exists such that G*H=F, you should output "no solution".