Description

Let us consider an n-dimension matching problem of two matrices. Here the index number of each dimension of a matrix starts at 1. For two n-dimension matrixes S and T, if there is a position (p₁, p₂, p₃, p₄, …,p_n) which satisfies that each element at the position (t₁, t₂, t₃, t₄, …,t_n) in T is the same as the element at the position (p₁ + t₁ - 1, p₂ + t₂ - 1, p₃ + t₃ - 1, p₄ + t₄ - 1, …,p_n + t_n - 1) in S, we call it’s a matching position. So the n-dimension problem is to compute the matching position for given S and T. You can assume that the traditional string matching problem is the 1-dimension version of this problem, and the normal matrix matching problem is the 2-dimension version.

Input

The first line contains the positive number n, which is not larger than 10.

The second line contains n positive numbers a₁, a₂, a₃, ...,a_n, representing the range of each dimension of matrix S.

The third line contains n positive numbers b₁, b₂, b₃, ...,b_n, representing the range of dimensions of matrix T.

The fourth line gives the elements in S.

The fifth line gives the elements in T.

To give out an n-dimension matrix with size c₁ * c₂ * c₃ * ... * c_n in a line, we will give the element at the position (d₁, d₂, d₃, …,d_n) in the matrix as the (c₂ * c₃ * ... * c_n * (d₁ – 1) + c₃ * c₄ * ... * c_n * (d₂ – 1) + ... + c_n * (d_{n - 1} – 1) + d_n)–th element in the line.

We guarantee that b_i <= a_i, elements in S and T are all positive integers that are not larger 100, and the number of the elements in S and T are both not larger than 500000.

Output

You should output n numbers in a line, p₁, p₂, p₃, …,p_n, representing the matching position. Please print the lexically smallest one if there are many. We guarantee that there is at least one matching position.

2
4 4
2 2
3 2 1 1 2 2 2 1 1 2 2 2 1 1 2 2
2 2 2 2

2 2

Source

POJ Monthly--2006.06.25, Long Fan