Practice Topology and Sorting with the exercise "nD-Vector sorting"

Learning Opportunities

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Statement

Goal

Given an n-dimensional topology space and a partial order definition, you'll need to sort a set of vectors in that topology space.

The topology space does not have a fixed number of dimensions, so you'll have to implement dimensions dynamically.

The ordering relation we will use is ascending order for each coordinate of each vector, following a permutation of coordinates given as input.
For instance, in a 3D space, with 2 3 1 as coordinates permutation, the vectors should be sorted first by their 2nd coordinate, then their 3rd, then their 1st.

Input

Line 1: An integer D for the number of dimensions
Line 2: An integer N for the number of vectors to sort
Line 3: D space separated integers representing the coordinate permutation to apply for the ordering.
Next N lines: D space separated integers representing the coordinate of a vector in this space.

Output

A single line containing N space separated integers representing the indexes of the input vectors, ordered by the given permuted ordering relation (ascending).

Indexation of vectors begins at 1 (input line 4).

Constraints

1 ≤ D ≤ 128
1≤ N ≤ 64
There are no duplicates in the input vectors

Example

Input

Output

2 1

Solve it

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