21802_Ahigh-dimensionalproble

As we all know, a point in n-dimensional space can be represented as a vector (x₁, x₂, ..., x_n), where x_i is a real number. Given a vector D = (d₁, d₂, ..., d_n), we can generate a series of planes perpendicular to D: each plane satisfies the condition that for any two point on the plane, say A = (a₁, a₂, ..., a_n), B = (b₁, b₂, ..., b_n), the inner product of (A - B) and D is zero, ie. (a₁ - b₁) × d₁ + (a₂ - b₂) × d₂ + ... + (a_n - b_n) × d_n = 0, and we call D the normal vector of the plane. let A × B denotes the inner product of A and B.

Here are n planes in n-dimensional space: S₁, S₂, ..., S_n with normal vector D₁, D₂, ..., D_n respectively. And P₁, P₂, ..., P_n lies on S₁, S₂,..., S_n respectively. We don't know the coordinates of P₁, P₂, ..., P_n, but instead we know D₁ × P₁, D₂ × P₂, ..., D_n × P_n. Can we find out the point of intersection of S₁, S₂, ..., S_n ?

There will be multiple test cases. Each data set will be formatted according to the following description:

1. A line containing two integers n, m, 3 ≤ n ≤ 100, 1 ≤ m ≤ n, m represents the number of queries to the same D₁, D₂, ..., D_n.

2. line 1 + i ( 1 ≤ i ≤ n) : n real number denoting the coordinates of D_i.

3. line 1 + n + i ( 1 ≤ i ≤ m): n real number denoting D₁ × P₁, D₂ × P₂, ..., D_n × P_n.

For each test data, there will be exactly m lines. For each query output a line containing the coordinates of the point of intersetion of S₁, S₂, ..., S_n. Round all the coordinates to the second digit after the decimal point. You may assume there will always be exactly one such point

3 1
1 0 0
0 1 0
0 0 1
1 1 1

1.00 1.00 1.00